Question

Can someone help me prove the identity?

Answer 1

See Explanation

Explanation:

`</p><p>\because \sin\bigg((\pi)/(2) + x\bigg)= \cos x\\</p><p>\&\: \sin (\pi - x) = \sin x\\\\</p><p></p><p>Now, </p><p></p><p>(\sin\bigg((\pi)/(2) + x\bigg))/(\sin (\pi - x)) = \cot x\\\\</p><p>LHS</p><p> = (\sin\bigg((\pi)/(2) + x\bigg))/(\sin (\pi - x)) \\\\</p><p>=(\cos x)/(sinx) \\\\</p><p>= \cot x\\\\</p><p>= RHS\\\\</p><p>Hence\: Proved </p><p>`