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العربية

prove (sec(x)cos(x))/(cot(x))=tan(x)

الحلّ

prove

\frac{sec ( x ) cos ( x )}{cot ( x )} = tan (x)

صحيح

خطوات الحلّ

\frac{sec ( x ) cos ( x )}{cot ( x )} = tan (x)

قم بالعمل على الطرف الأيسر

\frac{sec ( x ) cos ( x )}{cot ( x )}

sin, cos :

عبّر بواسطة

\frac{cos ( x ) sec ( x )}{cot ( x )}

sec (x) = \frac{1}{cos ( x )}

:Use the basic trigonometric identity

= \frac{cos ( x ) \frac{1}{c o s ( x )}}{cot ( x )}

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

:Use the basic trigonometric identity

= \frac{cos ( x ) \frac{1}{c o s ( x )}}{\frac{c o s ( x )}{s i n ( x )}}

\frac{cos ( x ) \frac{1}{c o s ( x )}}{\frac{c o s ( x )}{s i n ( x )}}

بسّط:

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

\frac{cos ( x ) \frac{1}{c o s ( x )}}{\frac{c o s ( x )}{s i n ( x )}}

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

: استخدم ميزات الكسور التالية

= \frac{cos ( x ) \frac{1}{c o s ( x )} sin ( x )}{cos ( x )}

cos (x) \frac{1}{cos ( x )} sin (x)

اضرب بـ:

sin (x)

cos (x) \frac{1}{cos ( x )} sin (x)

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

:اضرب كسور

= \frac{1 \cdot cos ( x ) sin ( x )}{cos ( x )}

cos (x) :

إلغ العوامل المشتركة

= 1 \cdot sin (x)

1 \cdot sin (x) = sin (x) :

اضرب

= sin (x)

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

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

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

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

:Use the basic trigonometric identity

= tan (x)

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

p ro v e 2 sin^{2} (\frac{9 θ}{2}) = 1 - cos (9 θ)

p ro v e cos (x) cos (x) = cos^{2} (x)

p ro v e 81 - 9 (3 sin (x))^{2} = - 1

p ro v e csc (x) + 1 = \frac{2}{sin ( x )}

p ro v e \frac{1}{cos ( x )} = arccos (x)