If sin x + cosec x = 2,

Given sin x + cosec x = 2

Squaring both sides, (sin x + cosec x)2 = 4

i. e $\sin ^{2} x+\operatorname{cosec}^{2} x+2 \sin x \operatorname{cosec} x=4$

i. e $\sin ^{2} x+\operatorname{cosec}^{2} x+2 \sin x \times \frac{1}{\sin x}=4$

i. e $\sin ^{2} x+\operatorname{cosec}^{2} x+2=4$

i. e $\sin ^{2} x+\operatorname{cosec}^{2} x=2$