Question

Prove that:-

Cos x Cos 2x cos 4x cos 8x=
Sin 16x/16 Sin x

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Answer 1

SOLUTION

Refer to the attachment

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Answer 2

Answer:

L.H.S. = R.H.S.

Step-by-step explanation:

Given :

$\large cos \ x \ cos \ 2 x \ cos \ 4 x \ cos 8 x = \dfrac{sin \ 16x}{16sin \x}$

$\large L.H.S.=cos \ x \ cos \ 2 x \ cos \ 4 x \ cos 8 x \\\\\\\large L.H.S.=\dfrac{1}{2}(2sin \ x \ cos \ x \ cos \ 2 x) \ cos \ 4 x \ cos 8 x \\\\\\\large \text{Multiply and divide by 2sin \ x }\\\\\\\large L.H.S.=\dfrac{2sin \ 2x \ cos \ 2 x \ cos \ 4 x \ cos 8 x }{4sin \ x} \\\\\\\large L.H.S.=\dfrac{2sin \ 4x \ cos \ 4 x \ cos 8 x }{8sin \ x}$

$\large L.H.S.=\dfrac{2sin \ 8x \ cos \ 8 x}{16sin \ x} \\\\\\\large L.H.S.=\dfrac{sin \ 16x}{16sin \ x}$

L.H.S. = R.H.S.

Hence proved.

Thus we get answer.