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شائع علم المثلثات >

tan(x-10)cot(20-x)=1

الحلّ

tan (x - 1 0^{\circ}) cot (2 0^{\circ} - x) = 1

الحلّ

x = 18 0^{\circ} n + 1 5^{\circ}, x = 10 5^{\circ} + 18 0^{\circ} n

راديان

x = \frac{π}{12} + πn, x = \frac{7 π}{12} + πn

خطوات الحلّ

tan (x - 1 0^{\circ}) cot (2 0^{\circ} - x) = 1

من الطرفين

1

اطرح

tan (x - 1 0^{\circ}) cot (2 0^{\circ} - x) - 1 = 0

tan (x - 1 0^{\circ}) cot (2 0^{\circ} - x) - 1

بسّط:

tan (\frac{18 x - 18 0 ^{\circ}}{18}) cot (\frac{18 0 ^{\circ} - 9 x}{9}) - 1

tan (x - 1 0^{\circ}) cot (2 0^{\circ} - x) - 1

tan (x - 1 0^{\circ}) cot (2 0^{\circ} - x) = tan (\frac{18 x - 18 0 ^{\circ}}{18}) cot (\frac{18 0 ^{\circ} - 9 x}{9})

tan (x - 1 0^{\circ}) cot (2 0^{\circ} - x)

x - 1 0^{\circ}

وحّد:

\frac{18 x - 18 0 ^{\circ}}{18}

x - 1 0^{\circ}

x = \frac{x 18}{18}

:حوّل الأعداد لكسور

= \frac{x \cdot 18}{18} - 1 0^{\circ}

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{x \cdot 18 - 18 0 ^{\circ}}{18}

= tan (\frac{18 x - 18 0 ^{\circ}}{18}) cot (- x + 2 0^{\circ})

2 0^{\circ} - x

وحّد:

\frac{18 0 ^{\circ} - 9 x}{9}

2 0^{\circ} - x

x = \frac{x 9}{9}

:حوّل الأعداد لكسور

= 2 0^{\circ} - \frac{x \cdot 9}{9}

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{18 0 ^{\circ} - x \cdot 9}{9}

= tan (\frac{18 x - 18 0 ^{\circ}}{18}) cot (\frac{- 9 x + 18 0 ^{\circ}}{9})

= tan (\frac{18 x - 18 0 ^{\circ}}{18}) cot (\frac{- 9 x + 18 0 ^{\circ}}{9}) - 1

tan (\frac{18 x - 18 0 ^{\circ}}{18}) cot (\frac{18 0 ^{\circ} - 9 x}{9}) - 1 = 0

sin, cos :

عبّر بواسطة

- 1 + cot (\frac{18 0 ^{\circ} - 9 x}{9}) tan (\frac{- 18 0 ^{\circ} + 18 x}{18})

cot (x) = \frac{cos ( x )}{sin ( x )}

:Use the basic trigonometric identity

= - 1 + \frac{cos ( \frac{18 0 ^{\circ} - 9 x}{9} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} )} tan (\frac{- 18 0 ^{\circ} + 18 x}{18})

tan (x) = \frac{sin ( x )}{cos ( x )}

:Use the basic trigonometric identity

= - 1 + \frac{cos ( \frac{18 0 ^{\circ} - 9 x}{9} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} )} \cdot \frac{sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

- 1 + \frac{cos ( \frac{18 0 ^{\circ} - 9 x}{9} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} )} \cdot \frac{sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

بسّط:

\frac{- sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} ) + cos ( \frac{18 0 ^{\circ} - 9 x}{9} ) sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

- 1 + \frac{cos ( \frac{18 0 ^{\circ} - 9 x}{9} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} )} \cdot \frac{sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

\frac{cos ( \frac{18 0 ^{\circ} - 9 x}{9} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} )} \cdot \frac{sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

اضرب بـ:

\frac{cos ( \frac{- 9 x + 18 0 ^{\circ}}{9} ) sin ( \frac{18 x - 18 0 ^{\circ}}{18} )}{sin ( \frac{- 9 x + 18 0 ^{\circ}}{9} ) cos ( \frac{18 x - 18 0 ^{\circ}}{18} )}

\frac{cos ( \frac{18 0 ^{\circ} - 9 x}{9} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} )} \cdot \frac{sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

:اضرب كسور

= \frac{cos ( \frac{18 0 ^{\circ} - 9 x}{9} ) sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

= - 1 + \frac{cos ( \frac{- 9 x + 18 0 ^{\circ}}{9} ) sin ( \frac{18 x - 18 0 ^{\circ}}{18} )}{sin ( \frac{- 9 x + 18 0 ^{\circ}}{9} ) cos ( \frac{18 x - 18 0 ^{\circ}}{18} )}

1 = \frac{1 sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

:حوّل الأعداد لكسور

= - \frac{1 \cdot sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )} + \frac{cos ( \frac{18 0 ^{\circ} - 9 x}{9} ) sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{- 1 \cdot sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} ) + cos ( \frac{18 0 ^{\circ} - 9 x}{9} ) sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

1 \cdot sin (\frac{18 0 ^{\circ} - 9 x}{9}) = sin (\frac{18 0 ^{\circ} - 9 x}{9}) :

اضرب

= \frac{- sin ( \frac{- 9 x + 18 0 ^{\circ}}{9} ) cos ( \frac{18 x - 18 0 ^{\circ}}{18} ) + cos ( \frac{- 9 x + 18 0 ^{\circ}}{9} ) sin ( \frac{18 x - 18 0 ^{\circ}}{18} )}{sin ( \frac{- 9 x + 18 0 ^{\circ}}{9} ) cos ( \frac{18 x - 18 0 ^{\circ}}{18} )}

= \frac{- sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} ) + cos ( \frac{18 0 ^{\circ} - 9 x}{9} ) sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}

\frac{- cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} ) sin ( \frac{18 0 ^{\circ} - 9 x}{9} ) + cos ( \frac{18 0 ^{\circ} - 9 x}{9} ) sin ( \frac{- 18 0 ^{\circ} + 18 x}{18} )}{cos ( \frac{- 18 0 ^{\circ} + 18 x}{18} ) sin ( \frac{18 0 ^{\circ} - 9 x}{9} )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos (\frac{- 18 0 ^{\circ} + 18 x}{18}) sin (\frac{18 0 ^{\circ} - 9 x}{9}) + cos (\frac{18 0 ^{\circ} - 9 x}{9}) sin (\frac{- 18 0 ^{\circ} + 18 x}{18}) = 0

Rewrite using trig identities

- cos (\frac{- 18 0 ^{\circ} + 18 x}{18}) sin (\frac{18 0 ^{\circ} - 9 x}{9}) + cos (\frac{18 0 ^{\circ} - 9 x}{9}) sin (\frac{- 18 0 ^{\circ} + 18 x}{18})

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

:فعّل متطابقة الطرح لزوايا

= sin (\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9})

sin (\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9}) = 0

sin (\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9}) = 0 :

حلول عامّة لـ

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 0 + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 18 0^{\circ} + 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 0 + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 18 0^{\circ} + 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 0 + 36 0^{\circ} n

حلّ:

x = 18 0^{\circ} n + 1 5^{\circ}

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 36 0^{\circ} n

اضرب بالمضاعف المشترك الأصغر

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 36 0^{\circ} n

Find Least Common Multiplier of

18, 9 : 18

18, 9

المضاعف المشترك الأصغر

18

تحليل لعوامل أوّليّة لـ:

2 \cdot 3 \cdot 3

18

18 = 9 \cdot 2, 2

ينقسم على

18

= 2 \cdot 9

9 = 3 \cdot 3, 3

ينقسم على

9

= 2 \cdot 3 \cdot 3

مركّب من أعداد أوّليّة فقط، لذلك تحليل إضافيّ غير ممكن

2, 3

= 2 \cdot 3 \cdot 3

9

تحليل لعوامل أوّليّة لـ:

3 \cdot 3

9

9 = 3 \cdot 3, 3

ينقسم على

9

= 3 \cdot 3

9

أو

18

احسب عدد مركّب من عوامل أوّليّة تظهر في

= 2 \cdot 3 \cdot 3

2 \cdot 3 \cdot 3 = 18 :

اضرب الأعداد

= 18

18 =

اضرب بالمضاعف المشترك الأصغر

\frac{- 18 0 ^{\circ} + 18 x}{18} \cdot 18 - \frac{18 0 ^{\circ} - 9 x}{9} \cdot 18 = 36 0^{\circ} n \cdot 18

بسّط

\frac{- 18 0 ^{\circ} + 18 x}{18} \cdot 18 - \frac{18 0 ^{\circ} - 9 x}{9} \cdot 18 = 36 0^{\circ} n \cdot 18

\frac{- 18 0 ^{\circ} + 18 x}{18} \cdot 18

بسّط:

- 18 0^{\circ} + 18 x

\frac{- 18 0 ^{\circ} + 18 x}{18} \cdot 18

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= \frac{( - 18 0 ^{\circ} + 18 x ) \cdot 18}{18}

18 :

إلغ العوامل المشتركة

= - - 18 0^{\circ} + 18 x

- \frac{18 0 ^{\circ} - 9 x}{9} \cdot 18

بسّط:

- 2 (- 9 x + 18 0^{\circ})

- \frac{18 0 ^{\circ} - 9 x}{9} \cdot 18

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= - \frac{( 18 0 ^{\circ} - 9 x ) \cdot 18}{9}

\frac{18}{9} = 2 :

اقسم الأعداد

= - 2 (- 9 x + 18 0^{\circ})

36 0^{\circ} n \cdot 18

بسّط:

648 0^{\circ} n

36 0^{\circ} n \cdot 18

2 \cdot 18 = 36 :

اضرب الأعداد

= 648 0^{\circ} n

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ}) = 648 0^{\circ} n

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ}) = 648 0^{\circ} n

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ}) = 648 0^{\circ} n

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ})

وسّع:

36 x - 54 0^{\circ}

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ})

- 2 (- 9 x + 18 0^{\circ})

وسٌع:

18 x - 36 0^{\circ}

- 2 (- 9 x + 18 0^{\circ})

a (b + c) = ab + a c

: افتح أقواس بالاستعانة بـ

a = - 2, b = - 9 x, c = 18 0^{\circ}

= - 2 (- 9 x) + (- 2) 18 0^{\circ}

فعّل قوانين سالب-موجب

- (- a) = a, + (- a) = - a

= 2 \cdot 9 x - 36 0^{\circ}

2 \cdot 9 = 18 :

اضرب الأعداد

= 18 x - 36 0^{\circ}

= - 18 0^{\circ} + 18 x + 18 x - 36 0^{\circ}

- 18 0^{\circ} + 18 x + 18 x - 36 0^{\circ}

بسّط:

36 x - 54 0^{\circ}

- 18 0^{\circ} + 18 x + 18 x - 36 0^{\circ}

جمّع التعابير المتشابهة

= 18 x + 18 x - 18 0^{\circ} - 36 0^{\circ}

18 x + 18 x = 36 x :

اجمع العناصر المتشابهة

= 36 x - 18 0^{\circ} - 36 0^{\circ}

- 18 0^{\circ} - 36 0^{\circ} = - 54 0^{\circ} :

اجمع العناصر المتشابهة

= 36 x - 54 0^{\circ}

= 36 x - 54 0^{\circ}

36 x - 54 0^{\circ} = 648 0^{\circ} n

انقل

54 0^{\circ}

إلى الجانب الأيمن

36 x - 54 0^{\circ} = 648 0^{\circ} n

للطرفين

54 0^{\circ}

أضف

36 x - 54 0^{\circ} + 54 0^{\circ} = 648 0^{\circ} n + 54 0^{\circ}

بسّط

36 x = 648 0^{\circ} n + 54 0^{\circ}

36 x = 648 0^{\circ} n + 54 0^{\circ}

36

اقسم الطرفين على

36 x = 648 0^{\circ} n + 54 0^{\circ}

36

اقسم الطرفين على

\frac{36 x}{36} = \frac{648 0 ^{\circ} n}{36} + 1 5^{\circ}

بسّط

\frac{36 x}{36} = \frac{648 0 ^{\circ} n}{36} + 1 5^{\circ}

\frac{36 x}{36}

بسّط:

x

\frac{36 x}{36}

\frac{36}{36} = 1 :

اقسم الأعداد

= x

\frac{648 0 ^{\circ} n}{36} + 1 5^{\circ}

بسّط:

18 0^{\circ} n + 1 5^{\circ}

\frac{648 0 ^{\circ} n}{36} + 1 5^{\circ}

\frac{36}{36} = 1 :

اقسم الأعداد

= 18 0^{\circ} n + 1 5^{\circ}

1 5^{\circ}

اختزل:

1 5^{\circ}

1 5^{\circ}

3 :

إلغ العوامل المشتركة

= 1 5^{\circ}

= 18 0^{\circ} n + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 18 0^{\circ} + 36 0^{\circ} n

حلّ:

x = 10 5^{\circ} + 18 0^{\circ} n

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 18 0^{\circ} + 36 0^{\circ} n

اضرب بالمضاعف المشترك الأصغر

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 18 0^{\circ} + 36 0^{\circ} n

Find Least Common Multiplier of

18, 9 : 18

18, 9

المضاعف المشترك الأصغر

18

تحليل لعوامل أوّليّة لـ:

2 \cdot 3 \cdot 3

18

18 = 9 \cdot 2, 2

ينقسم على

18

= 2 \cdot 9

9 = 3 \cdot 3, 3

ينقسم على

9

= 2 \cdot 3 \cdot 3

مركّب من أعداد أوّليّة فقط، لذلك تحليل إضافيّ غير ممكن

2, 3

= 2 \cdot 3 \cdot 3

9

تحليل لعوامل أوّليّة لـ:

3 \cdot 3

9

9 = 3 \cdot 3, 3

ينقسم على

9

= 3 \cdot 3

9

أو

18

احسب عدد مركّب من عوامل أوّليّة تظهر في

= 2 \cdot 3 \cdot 3

2 \cdot 3 \cdot 3 = 18 :

اضرب الأعداد

= 18

18 =

اضرب بالمضاعف المشترك الأصغر

\frac{- 18 0 ^{\circ} + 18 x}{18} \cdot 18 - \frac{18 0 ^{\circ} - 9 x}{9} \cdot 18 = 18 0^{\circ} 18 + 36 0^{\circ} n \cdot 18

بسّط

\frac{- 18 0 ^{\circ} + 18 x}{18} \cdot 18 - \frac{18 0 ^{\circ} - 9 x}{9} \cdot 18 = 18 0^{\circ} 18 + 36 0^{\circ} n \cdot 18

\frac{- 18 0 ^{\circ} + 18 x}{18} \cdot 18

بسّط:

- 18 0^{\circ} + 18 x

\frac{- 18 0 ^{\circ} + 18 x}{18} \cdot 18

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= \frac{( - 18 0 ^{\circ} + 18 x ) \cdot 18}{18}

18 :

إلغ العوامل المشتركة

= - - 18 0^{\circ} + 18 x

- \frac{18 0 ^{\circ} - 9 x}{9} \cdot 18

بسّط:

- 2 (- 9 x + 18 0^{\circ})

- \frac{18 0 ^{\circ} - 9 x}{9} \cdot 18

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= - \frac{( 18 0 ^{\circ} - 9 x ) \cdot 18}{9}

\frac{18}{9} = 2 :

اقسم الأعداد

= - 2 (- 9 x + 18 0^{\circ})

18 0^{\circ} 18

بسّط:

324 0^{\circ}

18 0^{\circ} 18

Apply the commutative law:

18 0^{\circ} 18 = 324 0^{\circ}

324 0^{\circ}

36 0^{\circ} n \cdot 18

بسّط:

648 0^{\circ} n

36 0^{\circ} n \cdot 18

2 \cdot 18 = 36 :

اضرب الأعداد

= 648 0^{\circ} n

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ}) = 324 0^{\circ} + 648 0^{\circ} n

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ}) = 324 0^{\circ} + 648 0^{\circ} n

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ}) = 324 0^{\circ} + 648 0^{\circ} n

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ})

وسّع:

36 x - 54 0^{\circ}

- 18 0^{\circ} + 18 x - 2 (- 9 x + 18 0^{\circ})

- 2 (- 9 x + 18 0^{\circ})

وسٌع:

18 x - 36 0^{\circ}

- 2 (- 9 x + 18 0^{\circ})

a (b + c) = ab + a c

: افتح أقواس بالاستعانة بـ

a = - 2, b = - 9 x, c = 18 0^{\circ}

= - 2 (- 9 x) + (- 2) 18 0^{\circ}

فعّل قوانين سالب-موجب

- (- a) = a, + (- a) = - a

= 2 \cdot 9 x - 36 0^{\circ}

2 \cdot 9 = 18 :

اضرب الأعداد

= 18 x - 36 0^{\circ}

= - 18 0^{\circ} + 18 x + 18 x - 36 0^{\circ}

- 18 0^{\circ} + 18 x + 18 x - 36 0^{\circ}

بسّط:

36 x - 54 0^{\circ}

- 18 0^{\circ} + 18 x + 18 x - 36 0^{\circ}

جمّع التعابير المتشابهة

= 18 x + 18 x - 18 0^{\circ} - 36 0^{\circ}

18 x + 18 x = 36 x :

اجمع العناصر المتشابهة

= 36 x - 18 0^{\circ} - 36 0^{\circ}

- 18 0^{\circ} - 36 0^{\circ} = - 54 0^{\circ} :

اجمع العناصر المتشابهة

= 36 x - 54 0^{\circ}

= 36 x - 54 0^{\circ}

36 x - 54 0^{\circ} = 324 0^{\circ} + 648 0^{\circ} n

انقل

54 0^{\circ}

إلى الجانب الأيمن

36 x - 54 0^{\circ} = 324 0^{\circ} + 648 0^{\circ} n

للطرفين

54 0^{\circ}

أضف

36 x - 54 0^{\circ} + 54 0^{\circ} = 324 0^{\circ} + 648 0^{\circ} n + 54 0^{\circ}

بسّط

36 x = 378 0^{\circ} + 648 0^{\circ} n

36 x = 378 0^{\circ} + 648 0^{\circ} n

36

اقسم الطرفين على

36 x = 378 0^{\circ} + 648 0^{\circ} n

36

اقسم الطرفين على

\frac{36 x}{36} = 10 5^{\circ} + \frac{648 0 ^{\circ} n}{36}

بسّط

\frac{36 x}{36} = 10 5^{\circ} + \frac{648 0 ^{\circ} n}{36}

\frac{36 x}{36}

بسّط:

x

\frac{36 x}{36}

\frac{36}{36} = 1 :

اقسم الأعداد

= x

10 5^{\circ} + \frac{648 0 ^{\circ} n}{36}

بسّط:

10 5^{\circ} + 18 0^{\circ} n

10 5^{\circ} + \frac{648 0 ^{\circ} n}{36}

10 5^{\circ}

اختزل:

10 5^{\circ}

10 5^{\circ}

3 :

إلغ العوامل المشتركة

= 10 5^{\circ}

= 10 5^{\circ} + \frac{648 0 ^{\circ} n}{36}

\frac{36}{36} = 1 :

اقسم الأعداد

= 10 5^{\circ} + 18 0^{\circ} n

x = 10 5^{\circ} + 18 0^{\circ} n

x = 10 5^{\circ} + 18 0^{\circ} n

x = 10 5^{\circ} + 18 0^{\circ} n

x = 18 0^{\circ} n + 1 5^{\circ}, x = 10 5^{\circ} + 18 0^{\circ} n

رسم

أمثلة شائعة

3csc(2x)-4sin(2x)=0

3 csc (2 x) - 4 sin (2 x) = 0

3tan(B)-4=tan(B)-2

3 tan (B) - 4 = tan (B) - 2

sin(2x)=5cos(2x)

sin (2 x) = 5 cos (2 x)

5sec(2x)+2=0

5 sec (2 x) + 2 = 0

2.1sin(θ)=1.33sin(θ+90)

2.1 sin (θ) = 1.33 sin (θ + 9 0^{\circ})