Evaluate: ^2 A+ ^2 A+ ^2 A - Vidyadip

Question

Evaluate: $\sin ^2 A+\cos ^2 A+\cot ^2 A$

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Answer

$\sin ^2 A+\cos ^2 A+\cot ^2 A ($Given$)$
We know that $\sin ^2 A+\cos ^2 A=1$
$\Rightarrow \sin ^2 A+\cos ^2 A+\cot ^2 A=1+\cot ^2 A$
$\Rightarrow \operatorname{cosec}^2 A\left(\text { Since } 1+\cot ^2 A=\operatorname{cosec}^2 A\right)$
Hence, $\sin ^2 A+\cos ^2 A+\cot ^2 A=\operatorname{cosec}^2 A$

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