Question

cosx 2 + cos 2 (x+π÷3) + cos2
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Answer 1

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Answer 2

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Formula to be used
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$= > \bf \cos ^{2} (x) = \frac{1 + \cos(2x) }{2}$
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$= > \cos ^{2} (x) + \cos ^{2} (x + \frac{\pi}{3} ) + \cos ^{2} (x - \frac{\pi}{3} ) \\ \\ = > \cos {}^{2} (x) + \frac{1 + \cos2(x + \frac{\pi}{3} ) }{2} + \frac{1 + \cos2(x - \frac{\pi}{3} ) }{2} \\ \\ = > \frac{2 \cos {}^{2} ( x ) + 1 + \cos2(x + \frac{\pi}{3} ) + 1 + \cos2( x - \frac{\pi}{3} ) }{2} \\ \\ = > \frac{1 + \cos(2x) + 2 + 2 \cos( \frac{2(x + \frac{\pi}{3} ) + 2(x - \frac{\pi}{3}) }{2} ) \cos( \frac{2(x + \frac{\pi}{3} )- (x - \frac{\pi}{3}) }{2} ) }{2} \\ \\ = > \frac{3 + \cos(2x) + 2 \cos(x + \frac{\pi}{3} + x - \frac{\pi}{3} ) \cos(x + \frac{\pi}{3} - x + \frac{\pi}{3} ) }{2} \\ \\ = > \frac{3 + \cos(2x) + 2 \cos(2x) \cos( \frac{2\pi}{3} ) }{2} \\ \\ = > \frac{3 + \cos(2x) + 2\cos(2x) \times ( - \frac{1}{2}) }{2} \\ \\ = > \frac{3 + \cos(2x) - \cos(2x) }{2 } \\ \\ = > \bf \underline{ \frac{3}{2} } \\ \\ \: \: \: \: \: \: \underline { < proved > }$
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