AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\cos ^4 \frac{\pi}{24}-\sin ^4 \frac{\pi}{24}=\)
- A \(\frac{\sqrt{2}-\sqrt{3}}{2}\)
- B \(\frac{\sqrt{2}+\sqrt{3}}{2}\)
- C \(\frac{\sqrt{2}-\sqrt{6}}{4}\)
- D \(\frac{\sqrt{2}+\sqrt{6}}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{\sqrt{2}+\sqrt{6}}{4}\)
Step-by-step Solution
Detailed explanation
\(\therefore \cos ^4 \frac{\pi}{24}-\sin ^4 \frac{\pi}{24}=\left(\cos ^2 \frac{\pi}{24}\right)^2-\left(\sin ^2 \frac{\pi}{24}\right)^2\) \(=\left(\cos ^2 \frac{\pi}{24}+\sin ^2 \frac{\pi}{24}\right)\left(\cos ^2 \frac{\pi}{24}-\sin ^2 \frac{\pi}{24}\right)\)…
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