AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=\)
- A \(2 \sec x\)
- B \(2 \operatorname{cosec} x\)
- C \(\tan 2 x\)
- D \(\sin 2 x\)
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…
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