Question

Evaluate $\frac{{\sec }^{2}36-{\cot }^{2}5}{{\csc }^{2}57-{\tan }^{2}33}+2{\sin }^{2}22{\cos }^{2}45{\sec }^{2}68$

Answer 1

$\frac{{\sec }^{2}36-{\cot }^{2}5}{{\csc }^{2}57-{\tan }^{2}33}+2{\sin }^{2}22{\cos }^{2}45{\sec }^{2}68$
$\frac{{\sec }^{2}36-\cot (90-36{)}^2}{\csc {90-33}^2-{\tan }^{2}33}+2{\sin }^{2}22(\frac{1}{\sqrt{2}}{)}^2\times \frac{1}{{\cos }^{2}68}$
$\frac{{\sec }^{2}36-{\tan }^{2}36}{{\sec }^{2}33-{\tan }^{2}33}+2\times \frac{1}{2}\frac{{\sin }^{2}22}{({\cos (90-22))}^2}$
$\frac{1}{1}+1\times \frac{{\sin }^2\left(22\right)}{{\sin }^2\left(22\right)}$
$1+(1\times 1)$
$1+1=2$