Question

The value of ${\tan }^2{30}^{\circ }+4{\sin }^2{45}^{\circ }+\frac{1}{3}{\cos }^2{30}^{\circ }$ is

• A. $2\frac{7}{12}$
• B. $1\frac{5}{12}$
• C. $-2\frac{5}{12}$
• D. $-1\frac{5}{12}$

Answer 1

The correct option is A $2\frac{7}{12}$

Given expression

${\tan }^{2}30+4{\sin }^{2}45+\frac{1}{3}{\cos }^{2}30$

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

$=\frac{1}{3}+2+\frac{1}{4}$

$=\frac{24+3+4}{12}$

$=2\frac{7}{12}$