TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(0 \lt B \lt A \lt \frac{\pi}{4}, \cos ^2 B-\sin ^2 A=\frac{\sqrt{3}+1}{4 \sqrt{2}}\) and \(2 \cos A \cos B=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}\), then \(\cos ^2 \frac{4 B}{3}-\sin ^2 \frac{4 A}{5}=\)
- A \(1\)
- B \(\frac{1}{2}\)
- C \(0\)
- D \(-\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\cos ^2 B-\sin ^2 A=\frac{\sqrt{3}+1}{4 \sqrt{2}}\) \(\cos (A-B) \cdot \cos (B+A)=\frac{\sqrt{3}+1}{2 \sqrt{2}} \cdot \frac{1}{2}\) ...(i) \(2 \cos A \cdot \cos B=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}\) \(\cos (A-B)+\cos (B+A)=\frac{1+\sqrt{3}}{2 \sqrt{2}}+\frac{1}{2}\)…
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