Question

If $\sin\theta + \text{cosec}\theta = 2,$ the value of $\sin^{10}\theta + \text{cose}\text{c}^{10}\theta$ is

• A. 10
• B. $2^{10}$
• C. $2^{9}$
• D. 2

Answer 1

Answer: (D)

2

Answer 2

We have, $\sin\theta + \text{cosec}\theta = 2$ $\Rightarrow$ $\sin^{2}\theta + 1 = 2\sin\theta$

$\Rightarrow$ $\sin^{2}\theta - 2\sin\theta + 1 = 0$

$\Rightarrow (\sin\theta - 1)^{2} = 0 \Rightarrow \sin\theta = 1$

Required value of $\sin^{10}\theta + \text{cose}\text{c}^{10}\theta = (1)^{10} + \frac{1}{(1)^{10}} = 2$.