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