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

The answer to whether csc^2(x/2)= 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 csc^2(x/2)= 2/(1-cos(x))

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

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

csc (θ) cos^{2} (θ) + sin (θ) = csc (θ)

sec (θ + \frac{π}{2}) = csc (θ)

\frac{1 + csc ( θ )}{sec ( θ )} - cot (θ) = cos (θ)

sin (2 θ) = \frac{2 cot ( θ )}{1 + cot ^{2} ( θ )}

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