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


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

(a) 1

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

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

(d) $\sqrt{3}$



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).


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