Q63 / 160 · AP EAMCET 2022 (08 Jul Shift 2) · Mathematics

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

  • A
    $\tan 2 x$
  • B
    $\operatorname{cosec} x$
  • Correct answer
    C
    $\sec x$
  • D
    $\cos 2 x$

Solution

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

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

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