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If sinx + sin 2 x + sin 3 x = 1,then find the value of cos 6 x - 4cos 4 x + 8cos 2 x.

If sinx + sin2x + sin3x = 1,then find the value of cos6x - 4cos4x + 8cos2x.

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
Write sinx + sin2x + sin3x = 1, as:
sinx +  sin3x = 1 – sin2x
Now squaring both sides,
U would get,
sin^6x + sin^4x + 3sin^2x = 1
and write each sin^2x to (1-cos^2x) 
=> (1-cos^2x) ^3 + (1-cos^2x)^2 + 3(1-cos^2x) = 1
  1. ould get further  cos6x - 4cos4x + 8cos2x. value as 1.

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