SOLUTION: Verify following is an identity. (1++sin(x))/sin(x)=(cot^2(x))/(csc(x)-1)

Question 396589: Verify following is an identity.
(1++sin(x))/sin(x)=(cot^2(x))/(csc(x)-1)

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Verify following is an identity.
(1++sin(x))/sin(x)=(cot^2(x))/(csc(x)-1)
Starting with the right hand side, notes:
(cot^2(x))/(csc(x)-1) =(cos^2/sin^2)/((1/sin)-1)
=(cos^2/sin^2)/(1-sin)/sin)
=(cos^2/sin^2)*(sin/(1-sin)) (invert and multiply)
=(cos^2/(sin)(1-sin)
=(1-sin^2)/(sin)(1-sin) (difference of 2 squares)
=(1+sin)(1-sin)/(sin)(1-sin) ((1-sin) cancels out)
=(1+sin)/sin
ans: right hand side=left hand side
RELATED QUESTIONS
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)

Verify following is an identity.... (answered by Alan3354)

Verify that cot^2 x + sin^2 x=csc^2 x is an identity (answered by Edwin McCravy)

please help me verify the following identity verify the identity: csc x [csc x... (answered by stanbon)

Verify following is an identity. (sin(x))(sec(x))/(sec(x)-1)=(sec(x)+1)cot(x) (answered by jsmallt9)

Verify the identity. (cot^2 x) / (cosec x + 1) = (1 - sin x) / sin x (answered by greenestamps)

Verify following is an identity... (answered by Tatiana_Stebko)

Verify following is an identity. tan^2(x)+1= (tan(x)/(cos(x))(sin(x)) (answered by lwsshak3)