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Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions2 Marks
Question
Prove that: $ \cos 4x = 1 - 8 \sin^2x \cos^2x$
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Answer

We have L.H.S. $= \cos 4x = 1 - 2 \sin^2 2x [\because \cos 2\theta = 1 - 2{\sin ^2}\theta ]$
$= 1 - 2 (2 \sin x \cos x)^2[\because \sin 2\theta = 2\sin \theta \cos \theta ]$
$= 1 - 2 (4 \sin^{2 }x \cos^2x)$
$= 1 - 8 \sin^2 x \cos^2 x =$ R.H.S.

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