Question

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

Answer 1

sin x = √2cosx - cosx = (√2 - 1) cosx

So, cos x = sin x/ (√2-1)

Now, sin²x + cos²x = 1

➝ (√2-1)²cos²x + cos²x = 1

➝ (3-2√2) cos²x + cos²x = 1

➝ (4-2√2)cos²x = 1

➝ cos²x = 1/(4-2√2) = (4+2√2)/8

➝ cos x = Root over ((4+2√2)/8)