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Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions2 Marks
Question
Prove that: cos 4x = 1 - 8sin2x cos2x
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Answer

We have L.H.S. = cos4x = 1 - 2sin22x $[\because \cos 2\theta = 1 - 2{\sin ^2}\theta ]$
= 1 - 2 (2sin x cosx)2 $[\because \sin 2\theta = 2\sin \theta \cos \theta ]$
= 1 - 2 (4sin2x cos2x)
= 1 - 8sin2x cos2x = R.H.S.

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