Question

Evaluate:

$\frac{{\cot }^2{30}^o+4{\sin }^2{45}^o+3{\sec }^2{30}^o+5{\cos }^2{90}^o}{\sec {60}^o+cosec{30}^o-{\tan }^2{60}^o}$.

Answer 1

Now,

$\frac{{\cot }^2{30}^o+4{\sin }^2{45}^o+3{\sec }^2{30}^o+5{\cos }^2{90}^o}{\sec {60}^o+cosec{30}^o-{\tan }^2{60}^o}$

$=\frac{(\sqrt{3}{)}^2+4\times \frac{1}{2}+3\times \frac{4}{3}+5\times 0}{2+2-(\sqrt{3}{)}^2}$

$=\frac{3+2+4+0}{2+2-3}$

$=9$.