If $$\sin \theta + cosec \theta = 2,$$ then the value of $$\sin^2 \theta + cosec^2 \theta$$ is:

Given,

$$\sin \theta + cosec \theta = 2$$

Squaring on both sides

$$\left(\sin\theta+\operatorname{cosec}\theta\right)^2=2^2$$

$$=$$>  $$\sin^2\theta+\operatorname{cosec}^2\theta+2\sin\theta\ \operatorname{cosec}\theta\ =4$$

$$=$$>  $$\sin^2\theta+\operatorname{cosec}^2\theta+2\sin\theta\ \frac{1}{\sin\theta\ }=4$$

$$=$$>  $$\sin^2\theta+\operatorname{cosec}^2\theta+2=4$$

$$=$$>  $$\sin^2\theta+\operatorname{cosec}^2\theta=4-2$$

$$=$$>  $$\sin^2\theta+\operatorname{cosec}^2\theta=2$$

Hence, the correct answer is Option B