Question

cosec a -sin a) (sec a- cos a) = 1/tan a + cot a ((((((((((((((((((((((((((((solve this question from LHS only​))))))))))))))))​

Answer 1

$(coseca - sina)(seca - cosa) \\ = ( \frac{1 - {sin}^{2} a}{sina} )( \frac{1 - {cos}^{2} a}{cosa} ) \\ = \frac{ {cos}^{2} a}{sina} \times \frac{ {sin}^{2} a}{cosa} \\ = sina \: cosa \\ = \frac{sina \: cosa}{ {sin}^{2} a + {cos}^{2}a } \\ = \frac{1}{ \frac{ {sin}^{2} a + {cos}^{2}a }{sina \: cosa} } \\ = \frac{1}{ \frac{sina}{cosa} + \frac{cosa}{sina} } \\ = \frac{1}{tana + cota}$