Correct Option: D

3 (sin x – cos x)⁴ + 6 (sinx + cos x)² + 4 (sin⁶x + cos⁶ x)
= 3 (sin²x + cos²x – 2 sinx . cosx)² + 6(sin²x + cos² x + 2 sinx . cosx ) + 4[(sin²x + cos²x)³ – 3 sin²x . cos²x (sin²x + cos²x)]
= 3 (1 – 2 sinx cosx)² + 6(1 + 2 sinx . cosx) + 4(1 – 3 sin²x cos²x)
= 3 (1 + sin²x . cos²x – 4 sinx cosx) + 6 (1+ 2 sinx cosx) + 4 (1 – 3 sin²x cos²x)
= 3 + 6 + 4 = 13