Question

If $\sin \, x + cosec \, x = 2$ then $\sin^n \, x + cosec^n \, x (n > 2)$ is equal to

• A. 2
• B. $2^n$
• C. $2^{n - 1}$
• D. none of these

Answer 1

Answer: (A)

2

Answer 2

Given $\sin x + cosec x = 2$ $\Rightarrow \sin x + \frac{1}{\sin x} = 2$ $\Rightarrow \sin^{2} x -2 \sin x + 1 = 0$ $\Rightarrow \left(\sin x -1\right)^{2} = 0$ $\Rightarrow \sin x = 1$ and hence $cosec \, x = 1$ $\therefore \sin^{n} x + cosec ^{n} x = 1^{n} + 1^{n} = 2.$