If x tan 45° cos 60° = sin 60°cot 60° then x = ?

As we know that,

$\tan 45^{\circ}=1$

$\cos 60^{\circ}=\frac{1}{2}$

$\sin 60^{\circ}=\frac{\sqrt{3}}{2}$

$\cot 60^{\circ}=\frac{1}{\sqrt{3}}$

By substituting these values, we get

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

$\Rightarrow x(1)\left(\frac{1}{2}\right)=\left(\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{3}}\right)$

$\Rightarrow \frac{x}{2}=\frac{1}{2}$

$\Rightarrow x=1$

Hence, the correct option is (a).