Question

How do you simplify `-cscθtanθsecθ`?

Answer 1

`-1/(cos^2(theta)`

Explanation:

Some basic definitions:
`color(white)("XXX")csc(theta) = 1/sin(theta)`

`color(white)("XXX")tan(theta) = sin(theta)/cos(theta)`

`color(white)("XXX")sec(theta) = 1/cos(theta)`

Therefore
`color(white)("XX")- cos(theta)*tan(theta)*sec(theta)`

`color(white)("XXX")= - 1/cancel(sin(theta))*cancel(sin(theta))/cos(theta)*1/cos(theta)`

`color(white)("XXX")= - 1/cos^2(theta)`