A) \[\cos \text{ec}\,x\]
B) \[\tan x\]
C) \[\cos x\]
D) \[\sec x\]
Correct Answer: D
Solution :
\[\frac{dy}{dx}=\frac{1}{\left( \frac{1+\sin x}{\cos x} \right)}\left[ \frac{\cos x\cos x+(1+\sin x)\sin x}{{{(\cos x)}^{2}}} \right]\] \[=\left( \frac{\cos x}{1+\sin x} \right)\frac{{{\cos }^{2}}x+{{\sin }^{2}}x+\sin x}{{{(\cos x)}^{2}}}=\sec x\].
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