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
- A \(\cos ^2 x\)
- B \(-\cos ^2 x\)
- C \(\cos ^2 x-1\)
- D \(\cos ^2 x-2\)
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, \(\cos x=\frac{2 \cos (x-y) \cos (x+y)}{\cos (x+y)+\cos (x-y)}\) \(\cos x=\frac{\cos 2 x+\cos 2 y}{2 \cos x \cdot \cos y}\) \(\cos x=\frac{2 \cos ^2 x+2 \cos ^2 y-2}{2 \cos x \cdot \cos y}\)…
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