SOLUTION: Prove the identity: {{{csc(x)+cot(x)=sin(x)/(1-cos(x))}}}

Algebra.Com
Question 148632: Prove the identity:

Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
Prove the identity:


Replace  on left side by 
Replace  on left side by 



Combine the numerators over the common denominator:



Form the conjugate of the numerator by changing the sign
of the second term:  , put it over itself,
like this , which equals 1,
so we can multiply by it without changing the value:



Indicate the multiplications of the tops and bottoms:



FOIL out the top:



Simplify by canceling in the top:





Replace  by 



The  in the bottom cancels out the
square in the top:





Edwin

RELATED QUESTIONS

Prove the identity csc x- cot x= sin x/1+ cos... (answered by lynnlo)
prove trigonometric identity (csc^2(x)-1)(sin(x))=... (answered by lwsshak3)
Prove the identity csc x- cos x cot x = sin... (answered by Fombitz,MathTherapy)
verify the identity 1.sin x sec x 2. cos x csc x =cot... (answered by stanbon)
(csc^2 x-1)sin x = cot x cos x verify the identity (answered by Alan3354)
prove trigonometric identity for... (answered by lwsshak3)
Prove this identity.... (answered by Alan3354)
prove that -sin(x)-cos(x)cot(x)=-csc(x) is an... (answered by mananth,Theo)
prove the identity sin x/tan x + cos x/cot x = sin x cos... (answered by edjones)