If √3sinθ-cosθ=2 then find the principal solution

Steps to solve If √3sinθ-cosθ=2 then find the principal solution

⇒√3sinθ-cosθ=2

⇒(√3sinθ-cosθ)/2=2/2

⇒(√3/2)sinθ-(1/2)cosθ=1

⇒cos(π/6).sinθ-sin(π/6).cosθ=1

⇒sin(θ-π/6)=sin(π/2)

⇒θ-π/6=π/2

⇒θ-π/6=nπ+(-1)^n(π/2)

⇒θ=nπ+(-1)^n(π/2)+π/6

⇒θ=nπ+(-1)^n (π/2)+π/6

⇒θ=0.π+(-1)^0 (π/2)+π/6=2π/3

Hence the principal solution of √3sinθ-cosθ=2 is 2π/3

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