Question
Prove the following identities:
$\cos^2\theta-\frac{1}{\big(1+\cot^2\theta\big)}=1$
$\cos^2\theta-\frac{1}{\big(1+\cot^2\theta\big)}=1$
✓
Answer
$\text{L.H.S.}=\cos^2\theta+\frac{1}{\big(1+\cot^2\theta\big)}$
$=\cos^2\theta+\frac{1}{\text{cosec}^2\theta}$
$=\cos^2\theta+\sin^2\theta$
$=1$
$=\text{R.H.S.}$
$=\cos^2\theta+\frac{1}{\text{cosec}^2\theta}$
$=\cos^2\theta+\sin^2\theta$
$=1$
$=\text{R.H.S.}$
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