SOLUTION: Verify following is an identity. (1-cos(x))/(1+cos(x))=(csc(x)-cot(x))^2 Thank you for helping me to solve trigeomertry

Question 396590: Verify following is an identity.
(1-cos(x))/(1+cos(x))=(csc(x)-cot(x))^2
Thank you for helping me to solve trigeomertry
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Verify following is an identity.
(1-cos(x))/(1+cos(x))=(csc(x)-cot(x))^2
Thank you for helping me to solve trigonometry
Starting with the right hand identity,
(csc(x)-cot(x))^2 = csc^2-2csc*cot+cot^2
= 1/sin^2-(2/sin)(cos/sin)+(cos/sin)^2
= 1/sin^2-(2cos)/sin^2+(sin)^2/(cos)^2
= (1-2cos+cos^2)/sin^2
= (cos-1)^2/(1-cos^2)
= (cos-1)(cos-1)/(1+cos)(1-cos)
= multiply both numerator and denominator by (-1)
= -(1-cos)(cos-1)/-(1+cos)(cos-1)
ans: = (1-cos)/(1+cos)
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