Q61 / 160 · AP EAMCET 2022 (07 Jul Shift 2) · Mathematics

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

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

Solution

$\begin{aligned} & \text { (b) } \frac{\sin x}{1+\cos x}=\frac{(\sin x)(1-\cos x)}{\sin ^2 x}=\operatorname{cosec} x-\cot x \\ & \text { and } \frac{1+\cos x}{\sin x}=\frac{1}{\operatorname{cosec} x-\cot x}=\operatorname{cosec} x+\cot x \\ & \therefore \quad \frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=2 \operatorname{cosec} x\end{aligned}$

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

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