SOLUTION: If sin x is not equal to zero, what is the solution of csc x - (cos x)(cot x)? What is the answer to sin (x - pi)?

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Question 3545: If sin x is not equal to zero, what is the solution of csc x - (cos x)(cot x)?
What is the answer to sin (x - pi)?
Found 2 solutions by longjonsilver, khwang:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
cosecX+=+%281%2FsinX%29 and cotX+=+%28cosX%2FsinX%29, so:

%281%2FsinX%29+-+cosX%28%28cosX%2FsinX%29%29

(1-cos^2X)/sinX

sin^2X/sinX --> this is why it says sinX is not zero, since if it was, we would have a "divide by zero" situation.

answer is therefore sinX

As for sin(x-pi)...what do you mean, what is the answer? You have not supplied an equation, so how can we help?

jon

Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean csc x = (cos x)(cot x)
or 1/sin x = cos x * cos x/sin x
or (1- cos^2 x)/sin x = 0,
or sin^2 x / sin x = 0
Since sin x <> 0, we have sin x = 0 (impossible)
Plz check your typing.
Whatever the given form is not so important.
You only need to simplify
(cos x)(cot x) = cos^2 x / sin x = (1-sin^2 x)/ sin x
and then try to solve by yourself.
Next, use sin (-A) = - sin A and sin(pi - A) = sin A.
We see that
sin(x -pi) = sin(-(pi -x)) = - sin(pi-x) = -sin x.
Kenny