Question

prove that tan A/cot A=sec^2A/cosec^2 A​

Answer 1

LHS=tan² A+cot² A

= sin² A + cos² A/cos² A + sin² A

= sin² A + cos² A/ sin² + cos² A

= (sin² A + cos² A )² - 2sin² A cos² A

sin² A cos² A

= 1 - 2sin² A cos² A/sin² A cos² A

= 1/cos² A. 1/sin² A - 2

= sec² A. cosec² A - 2

= RHS

Hope it helps you ｡●‿●｡