How do you express tan theta - cot^2theta in terms of cos theta ?

1 Answer
Jan 16, 2016

Explanation is given below.

Explanation:

tantheta - cot^2theta

On handiling these kind of problem apply your previous knowledge on identity.

tantheta = sintheta/costheta

cottheta = costheta/sintheta

sin^2theta = 1-cos^2theta

Our problem:

tantheta - cot^2theta

=sintheta/costheta - cos^2theta/sin^2theta

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

=(sqrt(1-cos^2theta)(1-cos^2theta))/(costheta(1-cos^2theta)) -(cos^2thetacostheta)/(costheta(1-cos^2theta)

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