COMEDK · Maths · 8. Trigonometric Ratios & Identities
\(\text { If } \dfrac{\cos x}{\cos (x-2 y)}=\lambda \text { then } \tan (x-y) \tan y=\)
- A \(\dfrac{\lambda}{1-\lambda}\)
- B \(\dfrac{1+\lambda}{1-\lambda}\)
- C \(\dfrac{1-\lambda}{1+\lambda}\)
- D \(\dfrac{\lambda}{1+\lambda}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{1-\lambda}{1+\lambda}\)
Step-by-step Solution
Detailed explanation
Given \(\dfrac{\cos x}{\cos (x-2y)} = \lambda\). Applying componendo and dividendo: \(\dfrac{\cos (x-2y) + \cos x}{\cos (x-2y) - \cos x} = \dfrac{1+\lambda}{1-\lambda}\) Using the sum-to-product formulas…
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