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 \(\cos ^2(\theta-\phi)=\)
- A \(\frac{3}{8}\)
- B \(\frac{5}{8}\)
- C \(\frac{3}{4}\)
- D \(\frac{5}{4}\)
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 \((\sin 2 \theta+\sin 2 \phi)^2=\frac{1}{4}\) \(\Rightarrow \sin ^2 2 \theta+\sin ^2 2 \phi+2 \sin 2 \theta \sin 2 \phi=\frac{1}{4}\)…
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