Question
Prove. $\cot^2 A - \cos^2 A = \cos^2 A.\cot^2 A$
✓
Answer
$\text { LHS }=\cot ^2 A-\cos ^2 A$
$=\frac{\cos ^2 A}{\sin ^2 A}-\cos ^2 A=\frac{\cos ^2 A\left(1-\sin ^2 A\right)}{\sin ^2 A}$
$=\cos ^2 A \frac{\cos ^2 A}{\sin ^2 A}=\cos ^2 A \cdot \cot ^2 A=\text { RHS }$
$=\frac{\cos ^2 A}{\sin ^2 A}-\cos ^2 A=\frac{\cos ^2 A\left(1-\sin ^2 A\right)}{\sin ^2 A}$
$=\cos ^2 A \frac{\cos ^2 A}{\sin ^2 A}=\cos ^2 A \cdot \cot ^2 A=\text { RHS }$
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