Question

If x tan ${45}^o$ cos ${60}^o$ = sin ${60}^o$ cot ${60}^o$ then x = ?

(a) 1 (b)$\frac{1}{2}$ (c) $\frac{1}{\sqrt{2}}$ (d) $\sqrt{3}$

Answer 1

$xtan{45}^{o}cos{60}^o=sin{60}^{o}cot{60}^o$

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

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

$\Rightarrow x=1$