Question:
If sin x + cosec x = 2, then sin2x + cosec2x = ___________ .
Solution:
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 $\sin ^{2} x+\operatorname{cosec}^{2} x=2$
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