Math, asked by rishabchandrago1709, 1 year ago

1+cos2x+cos4x + cos six x is equal to 4 cosx cos2x cos3x

Answers

Answered by AlonsoDehner
0

The proof can be done starting from right side.

Recall the formula

2 cos A cos B = cos (A+B)+cos (A-B)

and also cos 2A = 2cos^2 A-1

consider the right side

= 4 cos x cos 2x cos 3x

= 2(2cosx cos 3x) cos2x

= 2cos 2x [cos 4x+cos2x]

= 2 cos 2x cos 4x +2 cos ^2 2x

= [cos 6x + cos 2x] + 2 cos^2 2x

= cos 6x + cos 2x + 1 + cos 4x

= 1+cos 2x+cos 4x + cos 6x

Hence proved.

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