look below becaus it did not show up sorry!
It would have been nice for you to post what you were doing at the top of the page...
But no matter. You are trying to show:
sin(t) + cos(t)*cot(t) = csc(t)
Your algebra in line 3 of part B is incorrect. The rest is correct. Let's see what should happen in part B.
sin(t) + cos(t)/tan(t) = 1/sin(t)
sin(t) + cos(t)*cos(t)/sin(t) = 1/sin(t)
sin(t) + cos^2(t)/sin(t) = 1/sin(t)
Add the fractions on the LHS:
sin^2(t)/sin(t) + cos^2(t)/sin(t) = 1/sin(t)
[sin^2(t) + cos^2(t)]/sin(t) = 1/sin(t)
But sin^2(t) + cos^2(t) = 1, so...
1/sin(t) = 1/sin(t)
Since both sides are the same, we have an identity.
-Dan