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

Algebra ->  Trigonometry-basics -> SOLUTION: Prove the trigonometric identity: {{{csc(theta)}}}{{{""-""}}}{{{cot(theta)}}} = {{{sin(theta)/(1+cos(theta))}}}      Log On


   

Question 809257: Prove the trigonometric identity:
csc%28theta%29%22%22-%22%22cot%28theta%29 = sin%28theta%29%2F%281%2Bcos%28theta%29%29
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
csc%28theta%29%22%22-%22%22cot%28theta%29 ≟ sin%28theta%29%2F%281%2Bcos%28theta%29%29

1%2Fsin%28theta%29%22%22-%22%22cos%28theta%29%2Fsin%28theta%29

%281-cos%28theta%29%29%2Fsin%28theta%29

Multiply by fraction conjugate_of_numerator%2Fconjugate_of_numerator%29 = %281%2Bcos%28theta%29%29%2F%281%2Bcos%28theta%29%29

%281-cos%28theta%29%29%2Fsin%28theta%29%22%22%2A%22%22%281%2Bcos%28theta%29%29%2F%281%2Bcos%28theta%29%29

%281-cos%28theta%29%29%281%2Bcos%28theta%29%29%2Fsin%28theta%29%281%2Bcos%28theta%29%29%29

%281-cos%5E2%28theta%29%29%2Fsin%28theta%29%281%2Bcos%28theta%29%29%29

%28sin%5E2%28theta%29%29%2Fsin%28theta%29%281%2Bcos%28theta%29%29%29

%28sin%5Ecross%282%29%28theta%29%29%2Fcross%28sin%28theta%29%29%281%2Bcos%28theta%29%29%29

sin%28theta%29%2F%281%2Bcos%28theta%29%29

Edwin