Question 969502: Prove. (cotx-cscx)(cosx+1)=sinx
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! cot x=cos x/sin x; csc x=1/sinx
Rewrite in terms of sin x and cos x
(cos x/sin x)-(1/sin x) (cos x +1)
There is a common denominator, sin x
[(cos x-1)/sin x] (cos x +1). Now, multiply the first term by cos x and by +1
{(cos^2 x-cos x)/sin x} + (cos x- 1)/sin x
You have a common denominator of sin x
[cos^2 x- cos x + cos x -1]/sin x
In the numerator, the middle 2 terms disappear, and we have cos^2 x -1 left. But that is sin^2 x
because sin^2 x + cos ^2 x =1
we have sin^2 x/sin x . That equals sin x, which is the other side of the equation.
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