Question:
If x tan 45° cos 60° = sin 60°cot 60° then x = ?
(a) 1
(b) $\frac{1}{2}$
(c) $\frac{1}{\sqrt{2}}$
(d) $\sqrt{3}$
Solution:
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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