Question

If $xsin{45}^{\circ }co{s}^2{60}^{\circ }=\frac{ta{n}^2{60}^{\circ }cosec{30}^{\circ }}{sec{45}^{\circ }co{t}^2{30}^{\circ }}$, then x =

• A. 2
• B. 4
• C. 8
• D. 16

Answer 1

The correct option is C

8

We have:

$xsin{45}^{\circ }co{s}^2{60}^{\circ }=\frac{ta{n}^2{60}^{\circ }cosec{30}^{\circ }}{sec{45}^{\circ }co{t}^2{30}^{\circ }}$

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

$\Rightarrow \frac{x}{4\sqrt{2}}=\frac{6}{3\sqrt{2}}$

$\Rightarrow x=\frac{6}{3\sqrt{2}}$

$\Rightarrow x=\frac{6}{3\sqrt{2}}\times 4\sqrt{2}$

$\Rightarrow x=8$