Prove that cos2 x - cos2 x - -3 - cos2 x - -3 - 32

L.H.S. = cos^2x + cos^2 nbsp; nbsp; (x + π3 ) + cos^2 nbsp; nbsp; (x π3 ) = 1 + cos 2x2 + 1 + cos nbsp; nbsp; (2x + 2π3 )2 + 1 + cos nbsp; nb ...

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Prove that co...

Question

Prove that ${cos}^{2} x + {cos}^{2} (x + \frac{π}{3}) + {cos}^{2} (x - \frac{π}{3}) = \frac{3}{2}$

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{cos}^{2} x + {cos}^{2} (x + \frac{π}{3}) + {cos}^{2} (x - \frac{π}{3}) = \frac{3}{2}

f (x) = {cos}^{2} x + {cos}^{2} (x + \frac{π}{3}) + sin x sin (x + \frac{π}{3})

g (\frac{5}{4}) = 3

\frac{d}{d x} (g o f (x))

f (x) = {cos}^{2} x + {cos}^{2} (x + \frac{π}{3}) + {cos}^{2} (x - \frac{π}{3})

f^{'} (x) = 0

\frac{d y}{d x} + \frac{3}{{c o s}^{2} x} = \frac{1}{{c o s}^{2} x}, x ϵ (\frac{- π}{3}, \frac{π}{3}),

y (\frac{π}{4}) = \frac{4}{3},

y (- \frac{π}{4})

cos (2 x + \frac{π}{3})

x = \frac{π}{3}

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