Question

If $x\sin {45}^o{\cos }^2{60}^o=\frac{{\tan }^2{60}^o\csc {30}^o}{\sec {45}^o{\cot }^2{30}^o}$ then $x$ is equal to

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is C $8$

$x\sin {45}^o{\cos }^2{60}^o=\frac{{\tan }^2{60}^o\csc {30}^o}{\sec {45}^o{\cot }^2{30}^o}$

Substitute the respective trigonometric values

$x.\frac{1}{\sqrt{2}}\times \frac{1}{4}=\frac{3\times 2}{\sqrt{2}\times 3}$

$\frac{x}{4\sqrt{2}}=\sqrt{2}$

$x=4\times 2$

$\therefore x=8$