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