What am I doing wrong when verifying this identity

((1-cos)/(sin))=csc-cot

*I dropped the θ signs because they aren't currently necessary with what I'm dong.
** I DO know that is an identity, but I want to see the steps to prove it.

I keep looking at the power reducing and half angle formulas, but I feel like I'm skipping a step because I'm still not getting where I need to be in order to verify that this is an identity.

Any help is greatly appreciated. :]

Problem: ((1-cos)/(sin))=csc-cot

I worked the right hand side cause it looked easier to verify with.

csc - cot = 1/sin - cos/sin .... cause csc=1/sin, and cot=cos/sin ...... its all part of the trig. Identities

Since it has a common denominator, you combine the numerator together.

and you get 1 - cos/ sin

which equals to the left hand side of the problem.

1-cos/sin = 1-cos/sin


-Michael

P.S. And well, my teacher always taught me to do it on the left hand side of problem. But It just really depends what your teacher prefers you to do when working it out.

Remember that (a+b)/c = a/c + b/c

In this case a=1 b=-cos(θ) and c=sin(θ)

So you can rewrite it as

1/sin(θ) + -cos(θ)/sin(θ) = csc(θ) - cot(θ)

just split the fraction on the left, and you are virtually done!
(1-cos)/(sin))
= 1/sin - cos/sin
= csc - cot

(1 - cos) / sin = (1 / sin) - (cos / sin) = csc - cot