Question

theta and 3 theta minus 30 acute angles such that sin theta is equal to cos 3 theta minus 30 10 find the value of tan theta ​

Answer 1

θ and (3θ-30°) are acute angles such that 

sinθ=cos(3θ-30°)

or, sinθ=sin[90°-(3θ-30°)]   [∵, cosθ=sin(90°-θ)]

or, θ=90°-3θ+30°

or, θ+3θ=120°

or, 4θ=120°

or, θ=30°

∴, tanθ=tan30°=1/√3

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