Question

Find the value of ${\text{cosec}}^2{45}^o-{\cot }^2{45}^o$.

Answer 1

To find: ${\text{cosec}}^2{45}^o-{\cot }^2{45}^o$

${\text{cosec}}^2{45}^o-{\cot }^2{45}^o$

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

$=2-1$

$=1$

Hence, ${\text{cosec}}^2{45}^o-{\cot }^2{45}^o=1$