If sinθ + cosecθ = 2 then the value of $$\text{sin}^8\text{θ}+\text{cosec}^8\text{θ}$$​ is:

Correct option is A

Given:

​$$\sin\theta + \cosec\theta = 2$$

Concept Used:

​$$\cosec\theta = \frac{1}{\sin\theta}$$​​

Solution:
Let x = $$\sin\theta$$​, then $$\cosec\theta = \frac{1}{x}$$​​

So, When ​$$x + \frac{1}{x} = 2$$, then x must be equal to 1.

$$\text{sin}^8\text{θ}+\text{cosec}^8\text{θ}$$ = $$x^8 + \frac{1}{x^8} = 1^8 + 1^8 = 1 + 1 = 2$$​