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TS EAMCET · Maths · Trigonometric Ratios & Identities

\(\frac{\cos x}{\cos (x-2 y)}=\lambda \Rightarrow \tan (x-y) \tan y\) is equal to

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

Answer & Solution

Correct Answer

(B) \(\frac{1-\lambda}{1+\lambda}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} tan(x-y) \tan y=\frac{\sin (x-y) \sin y}{\cos (x-y) \cos y} \times \frac{2}{2} \\ =\frac{\cos (x-2 y)-\cos (x)}{\cos (x-2 y)+\cos (x)} \\ =\frac{1-\frac{\cos x}{\cos (x-2 y)}}{1+\frac{\cos (x)}{\cos (x-2 y)}} \\ =\frac{1-\lambda}{1+\lambda} \\ &\left(\text {…