Question

If sin θ + cos θ = √2 sin (90 – θ ), determine cos θ

Answer 1

Let the thetas be replaced by x.

sin x = √2 cos x - cos x [because sin(90°-x) = cos x]

=> sin x = cos x (√2-1)

=> sin x/(√2-1) = cos x

=> cos x = sin x/(√2-1)