Question
Prove that $\sec \theta(1-\sin \theta)(\sec \theta+\tan \theta)=1$
✓
Answer
$\text { LHS }=\sec \theta(1-\sin \theta)(\sec \theta+\tan \theta)$
$=\left[\sec \theta-\frac{\sin \theta}{\cos \theta}\right] \times(\sec \theta+\tan \theta)$
$=(\sec \theta-\tan \theta)(\sec \theta+\tan \theta)$
$=\sec ^2 \theta-\tan ^2 \theta$
$=1$
$=\text { RHS }$
$=\left[\sec \theta-\frac{\sin \theta}{\cos \theta}\right] \times(\sec \theta+\tan \theta)$
$=(\sec \theta-\tan \theta)(\sec \theta+\tan \theta)$
$=\sec ^2 \theta-\tan ^2 \theta$
$=1$
$=\text { RHS }$
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