Correct Option: D

3(sin x – cos x)⁴
= 3 (sin²x + cos²x – 2 sin x . cos x)²
= 3 (1 – 2sinx. cosx)²
= 3 (1 + 4 sin²x . cos²x – 4 sin x . cos x) 4 (sin⁶x + cos⁶x)
= 4 [(sin²x + cos²x)³ – 3 sin²x.cos²x (sin²x + cos²x) [a³ + b³ = (a+b)³ – 3ab (a+b)]
= 4 (1 – 3 sin²x . cos²x)
= 6 (sin x + cos x)²
= 6 (sin²x + cos²x+2 sin x. cos x)
= 6 (1 + 2 sin x . cos x)
∴ Expression = 3 (1 + 4sin²x . cos²x – 4sin x . cos x) + 4 (1 – 3sin²x . cos²x) + 6 (1 + 2sinx . cos x)
= 3 + 4 + 6 = 13