Question

cos 6x = 32 cos x - 48cos+ x + 18 cos2 x - 1.
25.
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Answer 1

Answer:

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Step-by-step explanation:

LHS = cos6x

= cos3(2x)

use, the formula,

cos3A = 4cos³A - 3cosA

= 4cos³(2x) - 3cos(2x)

use the formula,

cos2A = 2cos²A -1

= 4(2cos²x-1)³ - 3(2cos²x-1)

= 4{8cos^6x -3.(2cos²x)².1 +3.2cos²x.1² - 1 }-6cos²x +3

= 32cos^6x -48cos⁴x + 24cos²x -4 -6cos²x + 3

= 32cos^6x - 48cos⁴x +18cos²x -1 = RHS

Answer 2

Answer:

Using,

cos2x=2cos 2x−1cos3x=4cos 3x−3cosx

LHS:

cos6x=2cos 23x−1

=2(4cos 3x−3cosx) 2 −1

=2(16cos 6x+9cos 2x−24cos 4x)−1

=32cos 6x−48cos 4x+18cos 2 x−1 = RHS