Question

(cosec A -sin A )×(secA-cosA) ×(tanA+cotA)​

Answer 1

$\sf \underline{ \bigstar \: Solution \: : }$

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$\sf:\implies\: (cosecA - sinA) \: (secA - cosA) \: (tanA +cotA)$

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$\sf : \implies \: \left(\dfrac{1}{sinA} - sinA \right) \: \left( \dfrac{1}{cosA} - cosA\right) \: \left( \dfrac{sinA}{cosA} + \dfrac{cosA}{sinA} \right)$

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$\sf : \implies \: \dfrac{(1 - {sin}^{2}A) }{sinA} \: \dfrac{(1 - {cos}^{2}A) }{cosA} \: \left( \dfrac{sin {}^{2} A + cos {}^{2} A }{ {cos}A \: {sin} A} \right)$

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$\sf : \implies \: \dfrac{(cos {}^{2}A )}{sinA} \: \dfrac{(sin {}^{2}A )}{cos} \: \dfrac{1}{cosA \: sinA}$

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$\sf : \implies \: \cancel\dfrac{cosA \: sinA}{cosA \: sinA}$

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$\sf : \implies \: 1$

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$\sf \therefore \underline{Hence ,\: the \: solution \: is \: \bold{1}.}$