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AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=\)

  1. A \(2 \sec x\)
  2. B \(2 \operatorname{cosec} x\)
  3. C \(\tan 2 x\)
  4. D \(\sin 2 x\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(2 \operatorname{cosec} x\)

Step-by-step Solution

Detailed explanation

\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…