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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 42 of 61
Marks: +1, -0
cos 6x = 32 cos6cos^6 x – 48 cos4cos^4 x + 18 cos2cos^2 x – 1
Solution:  
We have, L.H.S. = cos 6x = cos 2(3x)
= 2 cos2cos^2 3x – 1 [Since cos2cos^2 θ = 2 cos2cos^2 θ – 1] = 2[(4cos3x–3cosx)2(4cos^3 x – 3 cosx)^2] –1
= 2[16 cos6xcos^6x + 9 cos2xcos^2x – 24 cos4xcos^4x] – 1 = 32 cos6xcos^6x – 48 cos4xcos^4x + 18 cos2xcos^2x – 1 = R.H.S.
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