If x tan 45° cos 60° = sin 60° cot 60°, then x is equal to
Question:

If $x \tan 45^{\circ} \cos 60^{\circ}=\sin 60^{\circ} \cot 60^{\circ}$, then $x$ is equal to

(a) 1

(b) $\sqrt{3}$

(c) $\frac{1}{2}$

(d) $\frac{1}{\sqrt{2}}$

Solution:

Given that: $x \tan 45^{\circ} \cos 60^{\circ}=\sin 60^{\circ} \cot 60^{\circ}$

Here we have to find the value of $x$

We know that $\left[\begin{array}{l}\tan 45^{\circ}=1 \\ \cos 60^{\circ}=\frac{1}{2} \\ \sin 60^{\circ}=\frac{\sqrt{3}}{2} \\ \cot 60^{\circ}=\frac{1}{\sqrt{3}}\end{array}\right]$

$\Rightarrow x \tan 45^{\circ} \cos 60^{\circ}=\sin 60^{\circ} \cot 60^{\circ}$

$\Rightarrow x \times 1 \times \frac{1}{2}=\frac{\sqrt{3}}{2} \times \frac{1}{\sqrt{3}}$

$\Rightarrow x=1$

Hence the correct option is $(a)$