Is 2/(1-cos(θ))=csc^2(θ/2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove 2/(1-cos(θ))=csc^2(θ/2)

prove

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

True

Solution steps

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

Let:

u = \frac{θ}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

csc (Θ) + sin (- Θ) = \frac{cos ^{2} ( Θ )}{sin ( Θ )}

cos (4 x) = cos^{2} (2 x) + sin^{2} (2 x)

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