Question

Solve: ${\sec }^2{45}^o+{\cot }^2{135}^o=$

Answer 1

${\sec }^2{45}^o+{\cot }^{(}{135}^o)$

$={\sec }^2{45}^o+{\cot }^2(180-{45}^o)$

$={\sec }^{2}45+(-\cot ({45}^o){)}^2$

$={\sec }^2{45}^o+{\cot }^2{45}^o$

$=(\sqrt{2}{)}^2+(1{)}^2$

$=2+1$

$=3$

$\therefore {\sec }^2{45}^o+{\cot }^2\left({135}^o\right)=3$.