Question
Prove that:
$\frac{\sin ^2 \theta}{\cos \theta}+\cos \theta=\sec \theta$
$\frac{\sin ^2 \theta}{\cos \theta}+\cos \theta=\sec \theta$
✓
Answer
Taking LHS
$\frac{\sin ^2 \theta}{\cos \theta}+\cos \theta$
$=\frac{\sin ^2 \theta+\cos ^2 \theta}{\cos \theta}$
$=\frac{1}{\cos \theta}\left[ As , \sin ^2 \theta+\cos ^2 \theta=1\right]$
$=\sec \theta\left[ As , \sec \theta=\frac{1}{\cos \theta}\right]$
= RHS
Proved !
$\frac{\sin ^2 \theta}{\cos \theta}+\cos \theta$
$=\frac{\sin ^2 \theta+\cos ^2 \theta}{\cos \theta}$
$=\frac{1}{\cos \theta}\left[ As , \sin ^2 \theta+\cos ^2 \theta=1\right]$
$=\sec \theta\left[ As , \sec \theta=\frac{1}{\cos \theta}\right]$
= RHS
Proved !
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