How do you simplify -cscθtanθsecθ?

1 Answer
Aug 23, 2015

-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)