AP EAMCET · Maths · Inverse Trigonometric Functions
If \(\cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}=k\) then \(\sin ^{-1}\left(\sqrt{\frac{k}{2}}\right)+\cos ^{-1}\left(\frac{k}{3}\right)=\)
- A \(\frac{2 \pi}{3}\)
- B \(\frac{3 \pi}{4}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{2 \pi}{3}\)
Step-by-step Solution
Detailed explanation
\(\cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}\) \(=\cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4\left(\frac{\pi}{2}+\frac{\pi}{8}\right)+\cos ^4\left(\frac{\pi}{2}+\frac{3 \pi}{8}\right)\)…
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