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Question: Answered & Verified by Expert
$\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=$
MathematicsTrigonometric Ratios & IdentitiesAP EAMCETAP EAMCET 2022 (07 Jul Shift 2)
Options:
  • A $2 \sec x$
  • B $2 \operatorname{cosec} x$
  • C $\tan 2 x$
  • D $\sin 2 x$
Solution:
2040 Upvotes Verified Answer
The correct answer is: $2 \operatorname{cosec} x$
$\begin{aligned} & \text { (b) } \frac{\sin x}{1+\cos x}=\frac{(\sin x)(1-\cos x)}{\sin ^2 x}=\operatorname{cosec} x-\cot x \\ & \text { and } \frac{1+\cos x}{\sin x}=\frac{1}{\operatorname{cosec} x-\cot x}=\operatorname{cosec} x+\cot x \\ & \therefore \quad \frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=2 \operatorname{cosec} x\end{aligned}$

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