Prove the following identity: ^2 A- ^2 A= ^2 A ^2 A - Vidyadip

Question

Prove the following identity:
$
\tan ^2 A-\sin ^2 A=\tan ^2 A \cdot \sin ^2 A
$

✓

Answer

$
\begin{aligned}
& \text { LHS }=\tan ^2 A-\sin ^2 A \\
& =\frac{\sin ^2 A}{\cos ^2 A}-\sin ^2 A=\frac{\sin ^2 A\left(1-\cos ^2 A\right)}{\cos ^2 A} \\
& =\frac{\sin ^2 A}{\cos ^2 A} \cdot \sin ^2 A=\tan ^2 A \cdot \sin ^2 A=\text { RHS }
\end{aligned}
$

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