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

1 Answer
May 18, 2018

tan thetatanθ

Explanation:

(csc theta)(sec theta - cos theta)(cscθ)(secθcosθ)
=(1/(sin theta))(1/(cos theta) - cos theta)=(1sinθ)(1cosθcosθ)
=1/(sin theta)(1/(cos theta) - ((cos theta)/1)((cos theta)/(cos theta)))=1sinθ(1cosθ(cosθ1)(cosθcosθ))
=1/(sin theta)(1/(cos theta) - (cos theta)^2/(cos theta))=1sinθ(1cosθ(cosθ)2cosθ)
=1/(sin theta)((1-(cos theta)^2) /(cos theta))=1sinθ(1(cosθ)2cosθ)
=1/(sin theta)((sin theta)^2/(cos theta))=1sinθ((sinθ)2cosθ)
=(sin theta)/(cos theta)=sinθcosθ

=tan theta =tanθ