Correct answer is A.
Given \(\frac{\text{sin 5x}}{\text{sin x}}\)
Let 5x = 3x + 2x
Then
[using sin (A+B) = sin A cos B + cos A sin B]
= (3 – 4 sin2x)(2 cos2x -1) + (4 cos3x – 3 cos x)(2 cosx)
= (6 cos2 x – 3 – 8 sin2 x cos2x + 4 sin2 x) + (8 cos4x - 6 cos2x)
[using sin2x + cos2x = 1]
= – 3 – 8 (1 - cos2x) cos2x + 4 (1 - cos2x)+ 8 cos4x
= – 3 – 8 cos2x + 8 cos4x + 4 - 4 cos2x + 8 cos4x
= 16 cos4x – 12 cos2x + 1