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

(a) 1

$$\begin{gathered} x\tan {45}^{\mathrm{o}}\cos {60}^{\mathrm{o}}=\sin {60}^{\mathrm{o}}\cot {60}^{\mathrm{o}} \\ \Rightarrow x\left(1\right)\left(\frac{1}{2}\right)=\left(\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{3}}\right) \\ \Rightarrow x\left(\frac{1}{2}\right)=\left(\frac{1}{2}\right) \\ \Rightarrow x=1 \end{gathered}$$