SOLUTION: Prove the following identity. cos2x/sinx = cscx-2sinx How do I go about this problem? I'm stuck on where to start and any help would be greatly appreciated.

Question 1126914: Prove the following identity.
cos2x/sinx = cscx-2sinx
How do I go about this problem? I'm stuck on where to start and any help would be greatly appreciated.
Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

start with left side and arrive to right side

.....since , we have

=

=

=...............since , we have

=

=

=.............since , we have
= -> we have arrived to right side

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
use cos^2 x- sin^2 x for cos2x
and cos^2 x=(1-sin^2 x)
so the left side becomes (1/sin x) (1-2 sin^2 x)
this is (1/sin x)(-2 sin x), dividing both terms by sin x.
or csc x-2 sin x
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