Question
Prove the following identities:
$\sec\theta(1-\sin\theta)(\sec\theta+\tan\theta)=0$
$\sec\theta(1-\sin\theta)(\sec\theta+\tan\theta)=0$
✓
Answer
$\text{L.H.S.}=\sec\theta(1-\sin\theta)(\sec\theta+\tan\theta)$ $=\Big[\sec\theta-\frac{\sin\theta}{\cos\theta}\Big]\times\big(\sec\theta+\tan\theta\big)$ $=(\sec\theta-\tan\theta)(\sec\theta+\tan\theta)$ $=\big(\sec^2\theta-\tan^2\theta\big)=1$ $=\text{R.H.S.}$$\therefore\ \text{L.H.S.}=\text{R.H.S}$
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