Question

prove : sec a / cosec² a - cosec a / sec² a = {(sin a × cos a + 1)(sin a - cos a)} / (cos a × sin a)​

Answer 1

$\frac{secA}{ {cosec}^{2}A } - \frac{cosecA}{ {sec}^{2} A} \\ = \frac{ {sin}^{2} A}{cosA} - \frac{ {cos}^{2} A}{sinA} \\ = \frac{ {sin}^{3} A - {cos}^{3}A }{sinA \: cosA} \\ = \frac{(sinA - cosA)( {sin}^{2}A + {cos}^{2} A + sinAcosA)}{sinAcosA} \\ = \frac{(sinA - cosA)(1 + sinAcosA)}{sinAcosA}$