Q. 133.8( 86 Votes )

Prove that cos<su

Answer :

To prove cos2 2x – cos2 6x = sin 4x sin 8x

RHS = sin 4x sin 8x


LHS = cos2 2x – cos2 6x


= (1 – sin2 2x) – (1 – sin2 6x)


= 1 – sin2 2x – 1 + sin2 6x


= sin2 6x – sin2 2x


= (sin 6x – sin 2x) (sin 6x + sin 2x)

[a2 – b2 = (a – b)(a + b)]





Rearranging we get


LHS = (2 × sin 2x × cos 2x)(2 × sin 4x × cos 4x)


LHS = sin 4x sin 8x


[
2sin A cos A = sin 2A]


LHS = RHS


Hence, proved.

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