JEE Mains · Maths · STD 11 - Trigonometrical equations
If \(L=\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)\) and \(M=\cos ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right),\) then
- A \(M =\frac{1}{2 \sqrt{2}}+\frac{1}{2} \cos \frac{\pi}{8}\)
- B \(L =\frac{1}{4 \sqrt{2}}-\frac{1}{4} \cos \frac{\pi}{8}\)
- C \(M =\frac{1}{4 \sqrt{2}}+\frac{1}{4} \cos \frac{\pi}{8}\)
- D \(L =-\frac{1}{2 \sqrt{2}}+\frac{1}{2} \cos \frac{\pi}{8}\)
Answer & Solution
Correct Answer
(A) \(M =\frac{1}{2 \sqrt{2}}+\frac{1}{2} \cos \frac{\pi}{8}\)
Step-by-step Solution
Detailed explanation
\(L =\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)\) \(\left(\because \sin ^{2} \theta=\frac{1-\cos 2 \theta}{2}\right)\) \(\Rightarrow L =\left(\frac{1-\cos (\pi / 8)}{2}\right)-\left(\frac{1-\cos (\pi / 4)}{2}\right)\)…
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