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) $\sqrt{3}$

Answer 1

As we know that,
​$$\begin{gathered} \tan 45°=1 \\ \cos 60°=\frac{1}{2} \\ \sin 60°=\frac{\sqrt{3}}{2} \\ \cot 60°=\frac{1}{\sqrt{3}} \\ \mathrm{By}\mathrm{substituting}\mathrm{these}\mathrm{values},\mathrm{we}\mathrm{get} \\ x\tan 45°\cos 60°=\sin 60°\cot 60° \\ \Rightarrow x\left(1\right)\left(\frac{1}{2}\right)=\left(\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{3}}\right) \\ \Rightarrow \frac{x}{2}=\frac{1}{2} \\ \Rightarrow x=1 \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{a}\right). \end{gathered}$$