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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(\cos (x-y), \cos x, \cos (x+y)\) are three distinct numbers which are in harmonic progression and \(\cos x \neq \cos y\), then \(1+\cos y\) is equal to

  1. A \(\cos ^2 x\)
  2. B \(-\cos ^2 x\)
  3. C \(\cos ^2 x-1\)
  4. D \(\cos ^2 x-2\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\cos ^2 x\)

Step-by-step Solution

Detailed explanation

\(\cos (x-y), \cos x, \cos (x+y)\) are in HP. Then, \(\cos x=\frac{2 \cos (x-y) \cos (x+y)}{\cos (x+y)+\cos (x-y)}\) \(\cos x=\frac{\cos 2 x+\cos 2 y}{2 \cos x \cdot \cos y}\) \(\cos x=\frac{2 \cos ^2 x+2 \cos ^2 y-2}{2 \cos x \cdot \cos y}\)…