Question

$pt. {sec}^{2} x + {cosec}^{2} x \geqslant 4$
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Solve the problem properly.

Answer 1

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✍
${sec}^{2} x + {cosec}^{2} x = (1 + {tan}^{2} x) + 1 + ( {cot}^{2} x) = 2 + {tan}^{2} x + {cot}^{2} x$

$2 + {tan}^{2} x + {cot}^{2} x - 2 \: tanx \: cotx + 2 \: tanx \: cot x$

$2 + (tanx - cotx) ^{2} + 2$

$4 + (tanx \: - \: cotx)^{2} \geqslant 4 \: \: \: \: \: \: \: \: \: \: \: \: \:[ (tanx - cotx) ^{2} \geqslant 0]$
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Answer 2

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refer to attachment !!

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