Question

costheta-sintheta/costheta+sintheta=1-√3/1+√3 find theta​

Answer 1

Refer to the above attachment

Answer 2

It has given that, (cosθ - sinθ)/(cosθ + sinθ) = (1 - √3)/(1 + √3)

we have to find the value of θ

solution : (cosθ - sinθ)/(cosθ + sinθ) = (1 - √3)/(1 + √3)

using Componendo and dividendo rule,

⇒[(cosθ - sinθ) + (cosθ + sinθ)]/[(cosθ + sinθ) - (cosθ - sinθ)] = [(1 - √3) + (1 + √3)]/[(1 + √3) - (1 - √3)]

⇒2cosθ/2sinθ = 2/2√3

⇒1/(sinθ/cosθ) = 1/√3

⇒tanθ = √3 = tanπ/3

⇒θ = π/3

Therefore the value of θ is π/3 (or 60°)