Question

The value of ${\sin }^2{30}^o{\cos }^2{45}^o+4{\tan }^2{30}^o+\frac{1}{2}{\sin }^2{90}^o-2{\cos }^2{90}^o$ is :

• A. $\frac{45}{24}$
• B. $\frac{46}{24}$
• C. $\frac{47}{24}$
• D. $\frac{49}{24}$

Answer 1

The correct option is C $\frac{47}{24}$

${\left(\frac{1}{2}\right)}^2\times {\left(\frac{1}{\sqrt{2}}\right)}^2+4{\left(\frac{1}{\sqrt{3}}\right)}^2+\frac{1}{2}{\left(1\right)}^2-2{\left(0\right)}^2$

$=\frac{1}{4}\times \frac{1}{2}+\frac{4}{3}+\frac{1}{2}=\frac{1}{8}+\frac{4}{3}+\frac{1}{2}$

$=\frac{3+32+12}{24}=\frac{47}{24}$