Question

Prove that:
1/1-cos theta+1/1+cos theta=2 cosec square theta

please don't spam otherwise I will spam you​

Answer 1

Answer:

you can do this by taking lcm 1-cos^2theta which is change to sin square theta

Answer 2

$\huge\green{To \ Prove:}$

$\sf{\frac{1}{1-cos\theta} + \frac{1}{1+cos\theta}=2cosec^{2}\theta}$

$\sf\blue{\underline{\underline{Proof:}}}$

$\sf{L.H.S.=\frac{1}{1-cos\theta}+\frac{1}{1+cos\theta}}$

$\sf{=\frac{1\times \ 1+cos\theta}{1-cos\theta\times \ 1+cos\theta}+\frac{1\times \ 1-cos\theta}{1+cos\theta\times \ 1-cos\theta}}$

$\sf{=\frac{1+cos\theta}{(1+cos\theta)(1-cos\theta)}+\frac{1-cos\theta}{(1+cos\theta)(1-cos\theta)}}$

$\sf{By \ identity}$

$\sf\pink{(a+b)(a-b)=a^{2}-b^{2}}$

$\sf{=\frac{1-cos\theta+1+cos\theta}{1-cos^{2}\theta}}$

$\sf{=\frac{2}{1-cos^{2}\theta}}$

$\sf\pink{By \ Trignometric \ identity}$

$\sf\pink{1-cos^{2}\theta=sin^{2}\theta}$

$\sf{=\frac{2}{sin^{2}\theta}}$

$\sf{By \ Trignometric \ ratio}$

$\sf\pink{\frac{1}{sin^{2}\theta}=cosec^{2}\theta}$

$\sf{=2cosec^{2}\theta}$

$\sf{=R.H.S.}$

$\sf{Hence, \ proved}$

$\sf\purple{\tt{\frac{1}{1-cos\theta}+\frac{1}{1+cos\theta}=2cosec^{2}\theta}}$