Question

If $\frac{x{\sin }^2{45}^o\times {\cos }^2{30}^o}{4{\cos }^2{60}^o}=\frac{3{\sin }^2{45}^o\times 2{\cos }^2{30}^o}{{\sin }^2{90}^o+2{\cos }^2{45}^o}$, then what is the value of $x$?

• A. 0
• B. 1
• C. 3
• D. 4

Answer 1

The correct option is C 3

Given,

$\frac{x{\sin }^{2}45\times {\cos }^{2}30}{4{\cos }^{2}60}=\frac{3{\sin }^{2}45\times 2{\cos }^{2}30}{{\sin }^{2}90+2{\cos }^{2}45}$

$\frac{x{\left(\frac{1}{\sqrt{2}}\right)}^2\times {\left(\frac{\sqrt{3}}{2}\right)}^2}{4{\left(\frac{1}{2}\right)}^2}=\frac{3{\left(\frac{1}{\sqrt{2}}\right)}^2\times 2{\left(\frac{\sqrt{3}}{2}\right)}^2}{(1{)}^2+2{\left(\frac{1}{\sqrt{2}}\right)}^2}$

$\frac{\frac{3x}{8}}{1}=\frac{\frac{9}{4}}{2}$

$\frac{3x}{8}=\frac{9}{8}$

$3x=9$

$\therefore x=3$