Question

If sin x + cosec x = 2, then sin²x + cosec²x = ___________ .

Answer 1

Given sin x + cosec x = 2
Squaring both sides, (sin x + cosec x)² = 4
$$\begin{gathered} \mathrm{i}.\mathrm{e}{\sin }^{2}x+{\mathrm{cosec}}^{2}x+2\sin x\mathrm{cosec}x=4 \\ \mathrm{i}.\mathrm{e}{\sin }^{2}x+{\mathrm{cosec}}^{2}x+2\sin x\times \frac{1}{\sin x}=4 \\ \mathrm{i}.\mathrm{e}{\sin }^{2}x+{\mathrm{cosec}}^{2}x+2=4 \\ \mathrm{i}.\mathrm{e}{\sin }^{2}x+{\mathrm{cosec}}^{2}x=2 \end{gathered}$$