sorry! it did not work
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