Question

If (Sinθ+Cosθ)²=2, then the value of θ is ​

Answer 1

(Sinθ + Cosθ)² = 2

Sin²θ + 2Cosθ.Sinθ + Cos²θ = 2

1 + 2sinθ.cosθ = 2

sin2θ = 2 - 1 = 1

sin2θ = 1

2θ = sin^(-1) (1)

θ = [sin^(-1)(1)] / 2

θ = (π/2)/2 = π/4

value for θ is π/4