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AP EAMCET · Maths · Trigonometric Ratios & Identities

\[
\frac{\cos x}{1+\sin x}+\tan x=
\]

  1. A 1
  2. B \(\cos x+\sin x\)
  3. C \(\sin ^2 x\)
  4. D \(\sec x\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\sec x\)

Step-by-step Solution

Detailed explanation

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