costheta-sintheta/costheta+sintheta=1-√3/1+√3 find theta
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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°)
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