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JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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If L=sin⁡2(π16)−sin⁡2(π8)L = {\sin ^2}\left( {\frac{\pi }{{16}}} \right) - {\sin ^2}\left( {\frac{\pi }{8}} \right) and M=cos⁡2(π16)−sin⁡2(π8), M = {\cos ^2}\left( {\frac{\pi }{{16}}} \right) - {\sin ^2}\left( {\frac{\pi }{8}} \right),\, then
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Correct option: D
M=122+12cos⁡π8M = \frac{1}{{2\sqrt 2 }} + \frac{1}{2}\cos \frac{\pi }{8}
Option D (M=122+12cos⁡π8M = \frac{1}{{2\sqrt 2 }} + \frac{1}{2}\cos \frac{\pi }{8}) is correct because it follows from applying trigonometric identities to simplify the expression for M.

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