Question

If $x$ tan ${45}^{\circ }.cot{60}^{\circ }=sin{30}^{\circ }.$ cosec ${60}^{\circ }$, then the value of $x$ is:

• A. $1$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $\sqrt{3}$

Answer 1

The correct option is A $1$

$x\tan {45}^0.\cot {60}^0=\sin {30}^0.\csc {60}^0$

$\Rightarrow x.1.\frac{1}{\sqrt{3}}=\frac{1}{2}\times \frac{2}{\sqrt{3}}$

$\Rightarrow x=1$

Hence, the answer is $1.$