Question

verify that (sinxcosx+cosx)/(sinx+sin^2x)=cotx

Answer 1

\[\Large \frac{\sin x \cos x + \cos x}{\sin x + \sin^2x}\quad=\]Factoring a cosine out of each top term, and a sine out of each bottom term gives us,
\[\Large \frac{\cos x(\sin x+1)}{\sin x(1+\sin x)}\quad=\]

Answer 2

Do you see the cancellation we can make from this spot?

Answer 3

(sinxcosx+cosx)/(sinx+sin^2x)
=cosx(sinx+1)/sinx(1+sinx)
=cosx/sinx
=cotx

Answer 4

yes! we can cancel out the (sinx-1) so that we get \[\frac{ \cos x }{ \sin x } \]

Answer 5

yes good :)