frac{sin x}{1+cos x} + frac{1+cos x}{sin x} = | vedclass

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Question

(B) Given expression: $\frac{\sin x}{1+\cos x} + \frac{1+\cos x}{\sin x}$ Taking the common denominator: $\frac{\sin^2 x + (1+\cos x)^2}{\sin x(1+\cos

Vedclass · Accepted Answer

$2 \operatorname{cosec} x$

Vedclass · Answer

(B) Given expression: $\frac{\sin x}{1+\cos x} + \frac{1+\cos x}{\sin x}$ Taking the common denominator: $\frac{\sin^2 x + (1+\cos x)^2}{\sin x(1+\cos x)}$ $= \frac{\sin^2 x + 1 + 2\cos x + \cos^2 x}{\sin x(1+\cos x)}$ Since $\sin^2 x + \cos^2 x = 1$,we get: $\frac{1 + 1 + 2\cos x}{\sin x(1+\cos x)}$ $= \frac{2 + 2\cos x}{\sin x(1+\cos x)} = \frac{2(1+\cos x)}{\sin x(1+\cos x)}$ $= \frac{2}{\sin x} = 2 \operatorname{cosec} x$

$\frac{\sin x}{1+\cos x} + \frac{1+\cos x}{\sin x} = ?$

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