Question

integrate (1+tan²x )/(1+tanx)​

Answer 1

Answer:

(1-tan x^2)/(1+tanx^2)

we know that 1+tanx^2 = secx^2, then the given term is

= (1-( sinx^2/cosx^2))/sec x^2

=((cosx^2-sinx^2)/cosx^2)/ secx^2

But secx^2 = 1/cosx^2

Therefore it can be simplified as

=((cosx^2 - sinx^2)/cosx^2)/(1/cosx^2)

= (( cosx^2-sinx^2)/cosx^2)*cosx^2

= cosx^2-sinx^2

Which equals cos2x

Therefore integral cos2x ,

=sin2x/2

Step-by-step explanation: