Question

cos2x cos2(x pi/3) cos2(x - pi/3) = 3/2. prove

Answer 1

LHS = Cos2x + Cos2(x+^/3) + Cos2(x-^/3)

  = (1+cosx)1/2 + (1+cos(x+^/3))1/2 + (1+cos(x-^/3)) 1/2 

  = 1/2 ( 1+cosx + 1 +Cos(x+^/3) + 1 + Cos(x-^/3)  )

  = 1/2 ( 3 + cosx + Cos( x + 60 ) + Cos( x - 60)

.  = 1/2 ( 3 + Cosx + 2 cosx cos120)

  = 1/2 ( 3 + cosx + 2 cosx . -1/2)  (since  cos 120 = -1/2)

  = 1/2 ( 3 + cosx - cosx)

  = 3/2 = RHS

  here , ^ means "pi"

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Answer 2

Hello Friend..❤️❤️

The answer of u r question is..✌️✌️


$cos2x \: cos2(x \frac{\pi}{3}) cos2(x - \frac{\pi}{3} ) = \frac{3}{2}$

Ans:✍️✍️✍️✍️✍️✍️✍️✍️✍️✍️

$lhs = cos2x + cos2( {x}^{ - 3} ) + cos2( {x}^{ - 3} )$

$= (1 + cosx) \frac{1}{2} + (1 + cos( {x}^{3} ) \frac{1}{2} (1 + cos {x}^{ - 3} ) \frac{1}{2}$


$= \frac{1}{2} (1 + cosx + 1 + cos {x}^{ + 3} ) + 1 + cos {x}^{ - 3}$

$= \frac{1}{2} (3 + cosx + cos(x + 60) + cos(x + - 60$

$= \frac{1}{2} (3 + cosx + 2cosx \: cos120)$

$= \frac{1}{2} (3 + cosx + 2cosx \frac{ - 1}{2}$


$= \frac{1}{2} (3 + cosx - cosx)$

$= \frac{3}{2}$


$hence \: proved$


Thank you..⭐️⭐️⭐️