How do you simplify (csc theta)(sec theta - cos theta)?

1 Answer
May 18, 2018

tan theta

Explanation:

(csc theta)(sec theta - cos theta)
=(1/(sin theta))(1/(cos theta) - cos theta)
=1/(sin theta)(1/(cos theta) - ((cos theta)/1)((cos theta)/(cos theta)))
=1/(sin theta)(1/(cos theta) - (cos theta)^2/(cos theta))
=1/(sin theta)((1-(cos theta)^2) /(cos theta))
=1/(sin theta)((sin theta)^2/(cos theta))
=(sin theta)/(cos theta)

=tan theta