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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(\frac{2 \sin \theta}{1+\cos \theta+\sin \theta}=y\), then \(\frac{1-\cos \theta+\sin \theta}{1+\sin \theta}=\)

  1. A \(y\)
  2. B \(\frac{1}{y}\)
  3. C \(1-y\)
  4. D \(1+y\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(y\)

Step-by-step Solution

Detailed explanation

\begin{gathered} y=\frac{2 \sin \theta}{1+\cos \theta+\sin \theta}=\frac{2\left(2 \sin \frac{\theta}{2} \cos \frac{\theta}{2}\right)}{2 \cos ^2 \frac{\theta}{2}+2 \sin \frac{\theta}{2} \cos \frac{\theta}{2}} \\ =\frac{2 \sin \frac{\theta}{2}}{\cos \frac{\theta}{2}+\sin…