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TS EAMCET · Maths · Trigonometric Equations

If \(\sin 2 \theta+\sin 2 \phi=\frac{1}{2}\) and \(\cos 2 \theta+\cos 2 \phi=\frac{3}{2}\), then \(\cos ^2(\theta-\phi)=\)

  1. A \(\frac{3}{8}\)
  2. B \(\frac{5}{8}\)
  3. C \(\frac{3}{4}\)
  4. D \(\frac{5}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{5}{8}\)

Step-by-step Solution

Detailed explanation

Given, \(\sin 2 \theta+\sin 2 \phi=\frac{1}{2}\) \(\cos 2 \theta+\cos 2 \phi=\frac{3}{2}\) Squaring on both Eqs. (i) and (ii), we get \((\sin 2 \theta+\sin 2 \phi)^2=\frac{1}{4}\) \(\Rightarrow \sin ^2 2 \theta+\sin ^2 2 \phi+2 \sin 2 \theta \sin 2 \phi=\frac{1}{4}\)…