Question

Write the acute angle θ satisfying√3 sin θ=cos θ.

Answer 1

SOLUTION :  

Given : √3 sin θ = cos θ

√3 sin θ = cos θ

sin θ = cos θ / √3

sin θ / cos θ = 1 / √3

tan θ = tan 30°  

[By using this identity , sin θ / cos θ = tan θ , tan 30° = 1 /√3]

On equating both sides,

θ =  30°  

Hence, the acute angle θ is  30° .

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Answer 2

you can solve it with this way also

÷ by 2 on both side
√3sin theta/2 - cos theta/2 = 0
sin(theta-30°) = 0
theta = 30°