Question

if sin theta + cos theta equal to root 2 then theta is equal to​

Answer 1

sin θ + cos θ = √2

Squaring on both sides,

(sin θ + cos θ)² = √2²

sin²θ + cos²θ + 2sinθ.cosθ = 2

1 + 2sinθ.cosθ = 2

2sinθ.cosθ = 2-1

2sinθ.cosθ = 1

sinθ.cosθ = ½

sinθ.cosθ = (1/√2) × (1/√2)

sinθ = cos θ = 1/√2

θ = 45°