Trig Identities Help!!

Why does sec x times cot x times sin^2x = sin x?
Just wondering because I got (Sinx)(sinx)/(cosx)(tanx) and i know that tanx = sinx/cosx so sinx = cosxtanx so does that means you cancel the sinx and cosx and tanx in the answer so that you are left with sinx?

By saying sinx = cosxtanx, you are making it too complicated. Always try and put everything in terms of cos and sin.

secx = 1/cosx (reciprocal), and cotx = cosx/sinx (quotient)

So:

(1/cosx) * (cosx/sinx) = (1/sinx) ....cosx cancels out

Then:

(1/sinx) * sin(^2)x, sinx in denominator cancels with one of the sinx's in the numerator, leaving only sinx, and verifying the identity.

Most people have a hard time with these at first. The trick is really just to get to know your identities like the back of your hand, because you need to eventually (by test time) be able to immediately recognize what identities might be applicable.

You say you got (Sinx)(sinx)/(cosx)(tanx).

Do you mean this? sin(x)sin(x)/[cos(x)tan(x)]
That would be equivalent to the left hand side.

sin(x)sin(x)/[cos(x)tan(x)]
= sin(x) [sin(x)/cos(x)] / tan(x)
= sin(x) tan(x)/tan(x)
= sin(x), for x ≠ kπ/2 for any integer k

The left and right sides are equivalent only under the constraint shown above, so it is not actually an identity.