3 का मूल्य (sin x - cos x)⁴ + 6 (sin x + cos x)² + 4 (sin⁶ x + cos⁶ x) is

3 (sinx – 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