Question
Prove. $sec^2 A + cosec^2 A = sec^2 A cosec^2 A$
✓
Answer
$\text { LHS }=\sec ^2 A +\operatorname{cosec}^2 A$
$=\frac{1}{\cos ^2 A}+\frac{1}{\sin ^2 A}=\frac{\sin ^2 A+\cos ^2 A}{\cos ^2 A \sin ^2 A}$
$=\frac{1}{\cos ^2 A \sin ^2 A}=\sec ^2 A \ \operatorname{cosec} 2=\text { RHS }$
$=\frac{1}{\cos ^2 A}+\frac{1}{\sin ^2 A}=\frac{\sin ^2 A+\cos ^2 A}{\cos ^2 A \sin ^2 A}$
$=\frac{1}{\cos ^2 A \sin ^2 A}=\sec ^2 A \ \operatorname{cosec} 2=\text { RHS }$
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