Question : If $0\leq\theta\leq 90^{\circ}$ and $4\cos^{2}\theta-4\sqrt{3}\cos\theta+3=0$, then the value of $\theta$ is:
Option 1: $30^{\circ}$
Option 2: $45^{\circ}$
Option 3: $90^{\circ}$
Option 4: $60^{\circ}$
Correct Answer: $30^{\circ}$
Solution :
Given: $4\cos^{2}\theta-4\sqrt{3}\cos\theta+3=0$
⇒ $(2\cos\theta-\sqrt3)^2=0$
⇒ $(2\cos\theta-\sqrt3)=0$
⇒ $2\cos\theta=\sqrt3$
⇒ $\cos\theta=\frac{\sqrt3}{2}$
⇒ $\cos\theta=\cos30^{\circ}$
So, $\theta=30^{\circ}$
Hence, the correct answer is $30^{\circ}$.
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