Question

show that sin square plus cosec square theta greater than equal to 2​

Answer 1

Please refer to this Attachment.

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Answer 2

$sin {}^{2} x + cosec {}^{2} x = 2 \\ cosec {}^{2} x \geqslant 1 + 1 - sin {}^{2} x \\ \frac{1}{sin {}^{2} x} \geqslant 1 + cos {}^{2} x \\ \frac{1}{sin {}^{2}x } - 1 \geqslant cos {}^{2} x \\ \frac{1}{sin {}^{2}x } \geqslant 1 \\ sin {}^{2} x \leqslant 1 \\ - 1 \leqslant sinx \leqslant 1 \\ value \: of \: sin \: lie \: bet \: - 1 \: and \: 1$