Prove that 3(sinx − cosx)^4 + 4(sin^6x − cos^6x) + 6(sinx + cosx)V2 = 13

Question

Prove that 3(sinx − cosx) ⁴ + 4(sin⁶x − cos⁶x) + 6(sinx + cosx)² = 13

Answer 1

 Let t₁, t₂, t₃ denote the three expressions on the left.

Therefore, t₁ + t₂ + t₃ = 3 + 4 + 6 = 13