Prove that ^2 A+cosec c^2 A = A+ A - Vidyadip

Question

Prove that$\sqrt{\sec ^2 A+\operatorname{cosec} c^2 A}=\tan A+\cot A$

✓

Answer

$\text { LHS }=\sqrt{\sec ^2 A+\operatorname{cosec}{ }^2 A} $
$=\sqrt{\frac{1}{\cos ^2 A}+\frac{1}{\sin ^2 A}} $
$ =\sqrt{\frac{\sin ^2 A+\cos ^2 A}{\sin ^2 A \cos ^2 A}} $
$ =\sqrt{\frac{1}{\sin ^2 A \cos ^2 A}} $
$ =\frac{1}{\sin A \cos A}$
$\text { RHS }=\tan A+\cot A $
$ =\frac{\sin A}{\cos A}+\frac{\cos A}{\sin A} $
$ =\frac{\sin ^2 A+\cos ^2 A}{\sin A \cos A} $
$ =\frac{1}{\sin A \cos A} $
$ \text { LHS }=\text { RHS }$

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