Prove the following identitie: (1 + tanA + secA)(1 + cotA - cosec… - Vidyadip

Question

Prove the following identitie:
(1 + tanA + secA)(1 + cotA - cosecA) = 2

✓

Answer

(1 + tanA + secA) (1 + cotA - cosecA)
=1 + cotA - cosecA + tanA + 1 - secA + secA + cosecA - cosecA secA
$=2+\frac{\cos A}{\sin A}+\frac{\sin A}{\cos A}-\frac{1}{\sin A \cos A}$
$=2+\frac{\cos ^2 A+\sin ^2 A}{\sin A \cos A}-\frac{1}{\sin A \cos A}$
$=2+\frac{1}{\sin A \cos A}-\frac{1}{\sin A \cos A}$
$=2$

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