The value of cos^2 frac{pi}{12} + cos^2 frac{ | vedclass

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Question

(A) Given expression: $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$We know that $\cos^2 	heta = \frac{1 + \cos(2	heta)}{2}

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$\frac{3}{2}$

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(A) Given expression: $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$We know that $\cos^2 	heta = \frac{1 + \cos(2	heta)}{2}$.Using this identity:$= \frac{1 + \cos(\frac{\pi}{6})}{2} + \cos^2(\frac{\pi}{4}) + \frac{1 + \cos(\frac{5\pi}{6})}{2}$$= \frac{1}{2} + \frac{1}{2}\cos(\frac{\pi}{6}) + (\frac{1}{\sqrt{2}})^2 + \frac{1}{2} + \frac{1}{2}\cos(\frac{5\pi}{6})$$= 1 + \frac{1}{2} + \frac{1}{2}(\cos \frac{\pi}{6} + \cos \frac{5\pi}{6})$Since $\cos(\frac{5\pi}{6}) = -\cos(\frac{\pi}{6})$:$= \frac{3}{2} + \frac{1}{2}(\cos \frac{\pi}{6} - \cos \frac{\pi}{6})$$= \frac{3}{2} + 0 = \frac{3}{2}$.

The value of $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$ is

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