Simplify the expression: frac{cos x}{1+sin x} | vedclass

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(D) We start with the expression: $\frac{\cos x}{1+\sin x} + 	an x$ Multiply the numerator and denominator of the first term by $(1-\sin x)$: $\frac{

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$\sec x$

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(D) We start with the expression: $\frac{\cos x}{1+\sin x} + 	an x$ Multiply the numerator and denominator of the first term by $(1-\sin x)$: $\frac{\cos x(1-\sin x)}{(1+\sin x)(1-\sin x)} + 	an x$ Using the identity $(1+\sin x)(1-\sin x) = 1-\sin^2 x = \cos^2 x$: $\frac{\cos x(1-\sin x)}{\cos^2 x} + 	an x$ Simplify the fraction: $\frac{1-\sin x}{\cos x} + 	an x$ Split the fraction: $\frac{1}{\cos x} - \frac{\sin x}{\cos x} + 	an x$ Since $\frac{1}{\cos x} = \sec x$ and $\frac{\sin x}{\cos x} = 	an x$: $\sec x - 	an x + 	an x = \sec x$

Simplify the expression: $\frac{\cos x}{1+\sin x} + \tan x$

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