Is sin^2(x/2)=(1-cos(x))/2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove sin^2(x/2)=(1-cos(x))/2

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

cos (x + \frac{3 π}{2}) = sin (x)

1 - tan^{4} (A) = 2 sec^{2} (A) - sec^{4} (A)

cos^{4} (θ) - sin^{4} (θ) = 2 cos^{2} (θ) - 1

sin (x) tan (x) + cos (x) = \frac{1}{cos ( x )}

\frac{1 - cos ( x )}{sin ( x )} = tan (\frac{x}{2})

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