Question

1+tan^2x/2tanx=?

Answer 1

`1+tanx/2`

Explanation:

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

=`1+(tanxtimestanx)/(2tanx)`

=`1+((cancel(tanx))(tanx))/(2 cancel tanx)`

=`1+tanx/2`

Answer 2

= csc 2x

Explanation:

`f(x) = (1 + tan^2 x) /(2tan x)`
Reminder:
`1 + tan^2 x = sec^2 x = 1/cos^2 x`
`f(x) = (1/(cos^2 x))/((2sin x)/(cos x)) = 1/(2sin x.cos x)`
`f(x) = 1/(sin 2x) = csc 2x`