Question : If $r\sin\theta=1$, $r\cos\theta=\sqrt{3}$, then the value of $(\sqrt{3}\tan\theta+1)$ is:
Option 1: $\sqrt{3}$
Option 2: $\frac{1}{\sqrt{3}}$
Option 3: $1$
Option 4: $2$
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Correct Answer: $2$
Solution :
Given: $r\sin\theta=1$, $r\cos\theta=\sqrt{3}$
$⇒\frac{r\sin\theta}{r\cos\theta}=\frac{1}{\sqrt{3}}$
$⇒\tan\theta=\frac{1}{\sqrt{3}}$
$⇒\sqrt{3}\tan\theta=1$
$\therefore\sqrt{3}\tan\theta+1=2$
Hence, the correct answer is $2$.
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