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Question -

Prove that: cos 4x = 1 – 8sincosx



Answer -

Consider

LHS = cos 4x

We can write it as

= cos 2(2x)

Using the formula cos2A = 1 – 2 sin2 A

= 1 – 2 sin2 2x

Again by using theformula sin2A = 2sin A cos A

= 1 – 2(2 sin x cos x2

So we get

= 1 – 8 sin2x cos2x

= R.H.S.

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