SOLUTION: 1/(1-cosx)-1/(1+secx) = csc^2x+cot^2x Can somebody help me do the following proof (solving from the left)? Thanks in advance!

Algebra ->  Geometry-proofs -> SOLUTION: 1/(1-cosx)-1/(1+secx) = csc^2x+cot^2x Can somebody help me do the following proof (solving from the left)? Thanks in advance!      Log On


   

Question 737632: 1/(1-cosx)-1/(1+secx) = csc^2x+cot^2x
Can somebody help me do the following proof (solving from the left)? Thanks in advance!
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%281-cosx%29-1%2F%281%2Bsecx%29+=+csc%5E2x%2Bcot%5E2x
LHS = 1%2F%281-cosx%29-1%2F%281%2Bsecx%29+

Take LCD
1%2F%281-cosx%29-1%2F%281%2B%281%2Fcosx%29%29%29+


1%2F%281-cosx%29-1%2F%28%281%2Bcosx%29%2Fcosx%29%29+


1%2F%281-cosx%29-cosx%2F%281%2Bcosx%29

%281%2Bcosx-cosx%281-cosx%29%29%2F%28%281%2Bcosx%29%281-cosx%29%29

%281%2Bcos%5E2%28x%29%29%2F%281-cos%5E2%28x%29%29

%281%2Bcos%5E2%28x%29%29%2F%28sin%5E2%28x%29%29

1%2Fsin%5E2%28x%29%2Bcos%5E2%28x%29%2Fsin%5E2%28x%29


cosec%5E2x%2Bcot%5E2x
LHS = RHS