Question

How do you prove that `(1+tanx)/(sinx+cosx)=secx`?

Answer 1

You can use the followings:
`tan(x)=sin(x)/cos(x)`
`sec(x)=1/cos(x)`

Giving:

`(1+sin(x)/cos(x))/(sin(x)+cos(x))=1/cos(x)`

`(cos(x)+sin(x))/cos(x)*1/(sin(x)+cos(x))=1/cos(x)`

simplifying:

`1/cos(x)=1/cos(x)`