Question

If $\sin A+\text{cosec}A=2,$ then the value of ${\sin }^{20}A+{\text{cosec}}^{20}A$ is

• A. $2$
• B. $20$
• C. $2^{20}$
• D. $1$

Answer 1

The correct option is A $2$

$\sin A+\text{cosec}A=2$
$\Rightarrow \sin A+\frac{1}{\sin A}=2$
$\Rightarrow (\sin A-1{)}^2=0$
$\Rightarrow \sin A=1$

${\sin }^{20}A+{\text{cosec}}^{20}A={\sin }^{20}A+\frac{1}{{\sin }^{20}A}$
$=1^{20}+\frac{1}{1^{20}}$
$=1+1=2$