How do you express sin theta - csc theta + sec theta in terms of cos theta ?

1 Answer
Jan 12, 2016

=(1-cos^3(theta))/(cos(theta)sqrt(1-cos^2(theta))

Explanation:

sin(theta) - csc(theta) + sec(theta)

=sin(theta)- 1/sin(theta) +1/cos(theta)

=(sin(theta)sin(theta)-1)/sin(theta) + 1/cos(theta)

=(sin^2(theta)-1)/sin(theta) + 1/cos(theta)

=-(1-sin^2(theta))/sin(theta) + 1/cos(theta)

=-cos^2(theta)/sin(theta) +1/cos(theta)

=(-cos^2(theta)*cos(theta))+1/(sin(theta)cos(theta))

=(-cos^3(theta)+1)/(cos(theta)sqrt(1-cos^2(theta))

=(1-cos^3(theta))/(cos(theta)sqrt(1-cos^2(theta))