Question

How do you simplify `secx(cosx+sinx)`?

Answer 1

`sec(x)(cos(x)+sin(x))=1+tan(x)`

Explanation:

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

Therefore
`sec(x)(cos(x)+sin(x))`
`color(white)("XXX")=1/cos(x)*cos(x)+1/cos(x)*sin(x)`

`color(white)("XXX")=1+sin(x)/cos(x)`

`color(white)("XXX")=1+tan(x)`