Question

The value of $\frac{6si{n}^2{45}^{\circ }+co{t}^2{60}^{\circ }+se{c}^2{30}^{\circ }}{tan{45}^{\circ }+cose{c}^2{60}^{\circ }}$ is

• A.
  $\frac{14}{3}$
  
• B.
  
  $\frac{13}{4}$
  
• C.
  
  $2$
• D.
  $1$

Answer 1

The correct option is C


$2$
$\frac{6si{n}^2{45}^{\circ }+co{t}^2{60}^{\circ }+se{c}^2{30}^{\circ }}{tan{45}^{\circ }+cose{c}^2{60}^{\circ }}=\frac{3+\frac{1}{3}+\frac{4}{3}}{1+\frac{4}{3}}=\frac{3+\frac{5}{3}}{\frac{7}{3}}=\frac{14}{3}\times \frac{3}{7}=2$

Hence, the correct answer is option (c).