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Question

Mathematics Question on Trigonometric Functions

cos⁡2π12+cos⁡2π4cos⁡25π12=\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} \cos^2 \frac{5 \pi}{12} =

A

32 \frac{3}{2}

B

3+32 \frac{3 + \sqrt{3} }{2}

C

23 \frac{2}{3}

D

23+3 \frac{2}{3 + \sqrt{3} }

Answer

32 \frac{3}{2}

Explanation

Solution

cos⁡2π12+cos⁡2π4cos⁡2π15\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} \cos^2 \frac{\pi}{15}
=cos⁡215∘+(12)2+cos⁡275∘= \cos^{2} 15^{\circ} + \left(\frac{1}{\sqrt{2} }\right)^{2} + \cos^{2} 75^{\circ}
=cos⁡215∘+sin⁡215∘+12=32= \cos^{2} 15^{\circ} +\sin^{2} 15^{\circ} + \frac{1}{2} = \frac{3}{2}