SOLUTION: I'm am trying to do a proof where (sinx - 2 + 1/sinx)/(sinx - 1/sinx) = (sinx - 1)/(sinx + 1) I have attempted to convert 1/sinx to cscx then cross multiply which ends up equalizi

Algebra ->  Trigonometry-basics -> SOLUTION: I'm am trying to do a proof where (sinx - 2 + 1/sinx)/(sinx - 1/sinx) = (sinx - 1)/(sinx + 1) I have attempted to convert 1/sinx to cscx then cross multiply which ends up equalizi      Log On


   

Question 840859: I'm am trying to do a proof where (sinx - 2 + 1/sinx)/(sinx - 1/sinx) = (sinx - 1)/(sinx + 1)
I have attempted to convert 1/sinx to cscx then cross multiply which ends up equalizing the top and bottom of the left hand side of the equation to 1 and I've also tried changing sinx -2 + 1/sinx to sin^2x/sinx + 1/sinx -2 over sin^2x/sinx - 1/sinx but then I just get stuck with the 2 in the way of everything. I'm just needing help on how to solve the problem and not just have the answer given to me
Answer by hamsanash1981@gmail.com(151) About Me  (Show Source):
You can put this solution on YOUR website!
LHS (sinx-2 +1/sinx)/(sinx - 1/sinx)
Evaluating numerator (sin^2x - 2sinx +1)/sinx => (Sin^2x -sinx -sinx +1)/sinx
Evaluating denominator (sin^2x - 1)/sinx
now combining numerator and deominator
=((sin^2x - sinx - sinx +1)/sinx )/((sin^2x -1)/sinx)
= ((sinx(sinx-1)-(sinx-1))/ (sin^2x-1)
= (sinx-1)(sinx-1)/(sinx-1)(sinx + 1)
=(sinx -1)/(sinx + 1)
= RHS