Question

Write the acute angle θ satisfying `sqrt(3) sin θ = cos θ`.

Answer 1

We have: `sqrt3 sinθ = cosθ`

⇒ `sqrt3 sin θ=cos θ` 

⇒ `sinθ/cos θ=1/sqrt3` 

⇒ `tan θ= tan 30°` 

⇒ `θ=30°` 

Hence the acute angle is 30°.