If sin θ + cos θ = 1, then find the general value of θ.

Given,

sin θ + cos θ = 1

We need to solve the above equation.

If we can convert this to a single trigonometric ratio, we can easily give its solution by using the formula.

∵ sin θ + cos θ = 1

⇒

⇒ {∵ sin(π/4)=cos(π/4) = 1/√2}

We know that: sin(A+B) = sinAcosB + cosAsinB

⇒

⇒

Formula to be used: If sin θ = sinα ⇒ θ = nπ + (-1)ⁿα

∴ θ + π/4 = nπ + (-1)ⁿ(π/4)

⇒ θ = nπ + (π/4)((-1)ⁿ – 1)