Question

If $0<\theta <90$ and $2\sin 2\theta =\sqrt{3},$ then find the value of $\theta .$

Answer 1

Given $0<\theta <90⟹0<2\theta <180$

$2\sin 2\theta =\sqrt{3}⟹\sin 2\theta =\frac{\sqrt{3}}{2}$

As $0<2\theta <180,$ $2\theta =60,120$

$⟹\theta =30,60$