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AP EAMCET · Maths · Trigonometric Equations

\(\tan x+\frac{\cos x}{1+\sin x}=\)

  1. A \(\tan 2 x\)
  2. B \(\operatorname{cosec} x\)
  3. C \(\sec x\)
  4. D \(\cos 2 x\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\sec x\)

Step-by-step Solution

Detailed explanation

\(\tan x+\frac{\cos x}{1+\sin x}\) \(\begin{aligned} & =\frac{\sin x}{\cos x}+\frac{\cos x}{1+\sin x} \\ & =\frac{\sin x+\sin ^2 x+\cos ^2 x}{\cos x(1+\sin x)} \\ & =\frac{(1+\sin x)}{\cos x(1+\sin x)}=\frac{1}{\cos x}=\sec x\end{aligned}\)