Question

Simplify tan2 θ(1 – cot2 θ).

Answer 1

\[\tan^2 \theta (1 - \cot ^2 \theta)?\]

Answer 2

Hmmm
I think
\[1+cot^2\theta=csc^2\theta\]
Since
\[sin^2\theta+cos^2\theta=1\]\[\frac{sin^2\theta}{sin^2\theta}+\frac{cos^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}\]\[1+cot^2\theta=csc^2\theta\]
So, the first post of @Australopithecus is not correct.., I think...

Answer 3

wait nope I'm wrong lol

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 4

\[tan^2 \theta (1-cot^2 \theta) = tan^2 \theta (1)- tan^2 \theta (cot^2 \theta) = tan^2 -1\]

Answer 5

For the last step, I missed a theta there... Sorry

Answer 6

I probably should have reviewed trig identites before attempting this

Answer 7

\[tan^2 \theta -1\] is just the answer for this question :|