Q63 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Mathematics

$$ \frac{\cos x}{1+\sin x}+\tan x= $$

  • A
    1
  • B
    $\cos x+\sin x$
  • C
    $\sin ^2 x$
  • Correct answer
    D
    $\sec x$

Solution

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

Hence, the correct answer is option: 'D'.

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