Question

(cosec a -sin a )(sec a - cos a)sec^2a= tan a
Prove lhs =rhs

Answer 1

$(cosec \: a \: - sin \: a)(sec \: a - cos \: a) {sec}^{2} a \\ \\ = ( \frac{1 - {sin}^{2}a }{sin \: a} )( \frac{1 - {cos}^{2}a }{cos \: a} ) {sec}^{2} a \\ \\ = ( \frac{ {cos}^{2}a }{sin \: a} )( \frac{ {sin}^{2}a }{cos \: a} ) ( \frac{1}{ {cos}^{2} a} )\\ \\ = \frac{sin \: a}{cos \: a} \\ = tan \: a$

=RHS