Question

How do you simplify (cos(x))/(sec(x)+tan(x))?

Answer 1

`(cos(x))/(sec(x)+tan(x))=color(blue)((cos^2(x))/(1+sin(x))`

Explanation:

From basic definitions:
`color(white)("XXX")sec(x)=1/cos(x)`
and
`color(white)("XXX")tan(x)=(sin(x))/(cos(x))`

Therefore
`color(white)("XXX")(cos(x))/(sec(x)+tan(x))`

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

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

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

`color(white)("XXX"XXX)=(cos^2(x))/(1+sin(x))`