Question

Question #f8601

Answer 1

RHS=LHS proves the identity

Explanation:

To prove the identity, it may be simpler to start with RHS.

RHS= `(tan(pi/4)+tan(A/2))/(1-tan(pi/4)tan(A/2))` =`(1+tan(A/2))/(1-tan(A/2)`

= `(cos(A/2)+sin (A/2))/(cos (A/2)- sin(A/2))` =`(cos(A/2)+sin (A/2))/(cos (A/2)- sin(A/2))* (cos(A/2)+sin (A/2))/(cos (A/2)+ sin(A/2))`

=`(cos^2 (A/2) +sin^2 (A/2) +2sin(A/2) cos( A/2))/(cos^2 (A/2) - sin^2 (A/2))`

`=(1+sinA)/cosA = secA +tan A= LHS`