NCERT Class XI Mathematics - Trigonometric Functions - Solutions

Question : 41

Total: 61

cos 4x = 1 – 8 sin2 x cos2 x

Solution:

We have, L.H.S.= cos 4x = cos 2(2x)
= 1 – 2 sin2 2x [Since cos2θ = 1 – 2 sin2θ]
= 1 – 2 (2sinxcosx)2 [Since sin 2θ = 2 sinθ cosθ]
= 1 – 2 [4 sin2 x cos2 x] = 1 – 8 sin2 x cos2 x = R.H.S.

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