Question

Solve equation root 3sin theta -cos theta =root 2

Answer 1

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Here is your answer...✌

√3sinθ - cosθ = √2

Dividing both sides by 2 , We get

( √3sinθ - cosθ ) / 2 = √2/2

(√3/2) sinθ - (1/2) cosθ = 1/√2

cos30° sinθ - sin30° cosθ = sin45°

sin( θ - 30° ) = sin45 °

[ using identity ,
sin(A-B) = sinAcosB - cosAsinB ]

⇒ θ - 30° = 45°

⇒ θ = 45° + 30°

⇒ θ = 75°

Answer 2

Answer:

√3cosθ+sinθ=2

⇒23cosθ+21sinθ=21

⇒sin(3π)cosθ+cos(3π)sinθ=21

⇒sin(3π+θ)=21

⇒3π+θ=nπ+(−1)n4π⇒θ=nπ+(−1)n4π−3π