Question

cos^4X - sin^4x / cosX - Sin X = surd 2sin(X+45)

Answer 1

Step-by-step explanation:

Cos⁴x - Sin⁴x / Cosx - Sinx

(Cos²x + Sin²x)(Cos²x - Sin²x) / Cosx - Sinx

1 (Cosx + Sinx)(Cosx - Sinx)/ (Cosx - Sinx)

Cosx + Sinx

Sin(90° + x) + Sinx

2 Sin(90° + 2x)/2 * Cos45°

2 Sin(45° + x) * 1/√2

= √2 Sin(x + 45°)