Mark the Correct alternative in the following:
is equal to
Given
Let 5x = 3x + 2x
Then
[using sin (A+B) = sin A cos B + cos A sin B]
[using the formulae :
sin 3x = 3sin x – 4 sin3x
cos 3x = 4 cos3x – 3 cos x
cos 2x = 2cos2x – 1
sin 2x = 2 sin x cos x ]
= (3 – 4 sin2x)(2cos2x -1) + (4 cos3x – 3cos x)(2cosx)
= (6cos2 x – 3 – 8 sin2 x cos2x + 4 sin2 x) + (8 cos4x - 6 cos2x)
[using sin2x + cos2 x = 1]
= – 3 – 8 (1 - cos2x) cos2x + 4 (1 - cos2x)+ 8cos4x
= – 3 – 8cos2x + 8cos4x + 4 - 4cos2x+8 cos4x
= 16 cos4x – 12 cos2x + 1
Therefore the answer is option A.