Is cos^2(1/2 x)= 1/2 (1+cos(x)) ?

The answer to whether cos^2(1/2 x)= 1/2 (1+cos(x)) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos^2(1/2 x)= 1/2 (1+cos(x))

prove

cos^{2} (\frac{1}{2} x) = \frac{1}{2} (1 + cos (x))

True

Solution steps

cos^{2} (\frac{1}{2} x) = \frac{1}{2} (1 + cos (x))

Let:

u = \frac{1}{2} x

cos^{2} (u) = \frac{1}{2} (1 + cos (2 u))

Prove

cos^{2} (u) = \frac{1}{2} (1 + cos (2 u)) :

True

Therefore

cos^{2} (\frac{1}{2} x) = \frac{1}{2} (1 + cos (x))

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) cos (θ) tan (θ) = 1 - cos^{2} (θ)

cot^{2} (- θ) + 1 = csc^{2} (θ)

\frac{1 - csc ^{2} ( t )}{csc ^{2} ( t )} = \frac{- 1}{sec ^{2} ( t )}

cot (θ) = cos (θ) csc (θ)

sech^{2} (x) = 1 - tanh^{2} (x)

Is cos^2(1/2 x)= 1/2 (1+cos(x)) ?
The answer to whether cos^2(1/2 x)= 1/2 (1+cos(x)) is True