Question

If $\sin A+\csc A=2$
find the value of ${\sin }^{2}A+{\csc }^{2}A$

Answer 1

Given $\sin A+\text{cosec}A=2$

Squaring on both sides

$(\sin A+\text{cosec}A{)}^2=4$

$⟹{\sin }^{2}A+{\text{cosec}}^{2}A+2\left(\sin A\right)\left(\text{cosec}A\right)=4$

$⟹{\sin }^{2}A+{\text{cosec}}^{2}A+2=4$

$⟹{\sin }^{2}A+{\text{cosec}}^{2}A=2$