ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

prove (3)((cos(2z))^2)/2 =(3cos(4z))/4

الحلّ

prove

(3) \frac{( cos ( 2 z ) ) ^{2}}{2} = \frac{3 cos ( 4 z )}{4}

الحلّ

خطأ

خطوات الحلّ

3 \cdot \frac{( cos ( 2 z ) ) ^{2}}{2} = \frac{3 cos ( 4 z )}{4}

لا يتساوى الطرفان

z = 0

عوّض

, 3 \frac{cos ^{2} ( 2 z )}{2} = \frac{3 cos ( 4 z )}{4}

في

3 \cdot \frac{cos ^{2} ( 2 \cdot 0 )}{2} = \frac{3}{2} (Decimal : 1.5)

3 \cdot \frac{cos ^{2} ( 2 \cdot 0 )}{2}

بسّط:

2 \cdot 0 = 0

2 \cdot 0

0 \cdot a = 0

فعّل القانون

= 0

3 \cdot \frac{cos ^{2} ( 0 )}{2} = \frac{3 cos ^{2} ( 0 )}{2}

3 \cdot \frac{cos ^{2} ( 0 )}{2}

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

:اضرب كسور

= \frac{cos ^{2} ( 0 ) \cdot 3}{2}

= \frac{3 cos ^{2} ( 0 )}{2}

استخدم المتطابقة الأساسيّة التالية:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= \frac{3 \cdot 1 ^{2}}{2}

بسّط

= \frac{3}{2}

\frac{3 cos ( 4 \cdot 0 )}{4} = \frac{3}{4} (Decimal : 0.75)

\frac{3 cos ( 4 \cdot 0 )}{4}

بسّط

= \frac{3 cos ( 0 )}{4}

استخدم المتطابقة الأساسيّة التالية:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= \frac{3 \cdot 1}{4}

بسّط

= \frac{3}{4}

لا يتساوى الطرفان

\Rightarrow خطأ

أمثلة شائعة

prove-2sin^2(x)+cos(x)+1=0

p ro v e - 2 sin^{2} (x) + cos (x) + 1 = 0

prove (2cot(u))/(csc^2(u)-2)=tan(2u)

p ro v e \frac{2 cot ( u )}{csc ^{2} ( u ) - 2} = tan (2 u)

prove csc(2x)+cot(2x)=(1+cos(2x))/(sin(2x))

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

prove 1-2sin^2(t)=2cos^2(t)-1

p ro v e 1 - 2 sin^{2} (t) = 2 cos^{2} (t) - 1

prove 1/(cos^2(θ))=sec^2(θ)

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