AP EAMCET · Maths · Trigonometric Ratios & Identities
\[
\frac{\cos x}{1+\sin x}+\tan x=
\]
- A 1
- B \(\cos x+\sin x\)
- C \(\sin ^2 x\)
- D \(\sec x\)
Answer & Solution
Correct Answer
(D) \(\sec x\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{\cos x}{1+\sin x}+\tan x \\ & =\frac{\cos x(1-\sin x)}{(1+\sin x)(1-\sin x)}+\tan x \\ & =\frac{\cos x \times(1-\sin x)}{1-\sin ^2 x}+\tan x=\frac{1-\sin x}{\cos x}+\tan x \\ & =\sec x-\tan x+\tan x=\sec x\end{aligned}\)
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