Prove that: ^2 (1+ ^2 )=1 - Vidyadip

Question

Prove that:
$\cos ^2 \theta\left(1+\tan ^2 \theta\right)=1$

✓

Answer

Taking LHS
$\begin{array}{l}\cos ^2 \theta\left(1+\tan ^2 \theta\right) \\
=\cos ^2 \theta \sec ^2 \theta\left[\text { As, } \sec ^2 \theta=1+\tan ^2 \theta\right] \\
=\cos ^2 \theta \times \frac{1}{\cos ^2 \theta}\left[\text { As, } \sec \theta=\frac{1}{\cos \theta}\right] \\
=1 \\
=\text { RHS }
\end{array}$
Proved!

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