Prove the following identity: cos x + cos 2x + cos 3x = cos 2x(1 + 2cos x)

Expert Answers

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We have to prove : cos x + cos 2x + cos 3x = cos 2x(1 + 2cos x)

We know that cos A + cos B = 2 * cos (A + B)/2 * cos (A − B)/2

Now cos x + cos 2x + cos 3x

=> 2 * cos (4x / 2) * cos (2x / 2) + cos 2x

=> 2 cos 2x * cos x + cos 2x

=> cos 2x ( 1 + 2 cos x)

Therefore we prove that

cos x + cos 2x + cos 3x = cos 2x(1 + 2cos x)

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