Question

Evaluate $\frac{2{\cos }^2{90}^o+4{\cos }^2{45}^o+{\tan }^2{60}^o+3cs{c}^2{60}^o+1}{3csc{60}^o-\frac{7}{2}{\sec }^2{45}^o+2\csc {30}^o-1}$

Answer 1

Consider the following question.

$\frac{2{\cos }^2{90}^0+4{\cos }^2{45}^0+{\tan }^2{60}^0+3{\csc }^2{60}^0+1}{3\csc {60}^0-\frac{7}{2}{\sec }^{2}45+2\csc {30}^0-1}$

$=\frac{2\ast 0+4{\left(\frac{1}{\sqrt{2}}\right)}^2+{\left(\sqrt{3}\right)}^2+3{\left(\frac{2}{\sqrt{3}}\right)}^2+1}{3{\left(\frac{2}{\sqrt{3}}\right)}^2-\frac{7}{2}{\left(\sqrt{2}\right)}^2-1}$

$=-2$

Hence, this is the required answer.