Question

prove that tana/1+seca - tan/1- sec a =2 cosec a​

Answer 1

Step-by-step explanation:

tan a/1+sec a - tan a/ 1-sec a =2cosec a

LHS=tan a (1-sec a)-tan a ( 1+sec a)/1-sec^2 a ( a^2+ b^2=(a+b)(a-b)

=tan a (1- sec a-1- sec a)/tan^2 a

=2sec a/tan a=2 1/cos a × cos a/sin a

=2/ sin a

=2cosec a = RHS