Question

If $\sin x+cosecx=2,$ then $({\sin }^{10}x+cose{c}^{10}x)$ is equal to:

• A. 3
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (D)

2

$\sin x+cosecx=2$
$\Rightarrow \sin x+\frac{1}{\sin x}=2$
$\Rightarrow {\sin }^{2}x+1=2\sin x$
$\Rightarrow {\sin }^{2}x-2\sin x+1=0$
$\Rightarrow (\sin x-1{)}^2=0$
$\Rightarrow \sin x=1$
$cosecx=1$
${\sin }^{10}x+cose{c}^{10}x=2$