SOLUTION: Why 1-sin^2x/sinx-cscx? is -sinx??? I thought it was sinx, but the answer says -sinx, how do you get that - ? I found this answer online, but I still don't get how they got tha

Algebra ->  Trigonometry-basics -> SOLUTION: Why 1-sin^2x/sinx-cscx? is -sinx??? I thought it was sinx, but the answer says -sinx, how do you get that - ? I found this answer online, but I still don't get how they got tha      Log On


   

Question 978241: Why 1-sin^2x/sinx-cscx? is -sinx??? I thought it was sinx, but the answer says -sinx, how do you get that - ?
I found this answer online, but I still don't get how they got that negative answer at the end, why he multiplied that times -1 ?
1 - sin ² x
--------------
sin x - csc x
1 - sin ² x
--------------------
sin x - 1/sin x
sin x ( 1 - sin ² x )
--------------------------
sin ² x - 1
- ( sin ² x - 1 ) sin x
----------------------------
sin ² x - 1
- sin x
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with lefthand side,
cos%5E2%28x%29%2F%28sin%28x%29-csc%28x%29%29

cos%5E2%28x%29%2F%28sin%28x%29-1%2Fsin%28x%29%29

cos%5E2%28x%29%2F%28sin%28x%29sin%28x%29%2Fsin%28x%29-1%2Fsin%28x%29%29

cos%5E2%28x%29%2F%28%28sin%5E2%28x%29-1%29%2Fsin%28x%29%29

cos%5E2%28x%29%2F%28%281-cos%5E2%28x%29-1%29%2Fsin%28x%29%29

cos%5E2%28x%29%2F%28-cos%5E2%28x%29%2Fsin%28x%29%29

1%2F%28-1%2Fsin%28x%29%29
and you can see the last step...

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Why 1-sin^2x/sinx-cscx? is -sinx??? I thought it was sinx, but the answer says -sinx, how do you get that - ?
I found this answer online, but I still don't get how they got that negative answer at the end, why he multiplied that times -1 ?
1 - sin ² x
--------------
sin x - csc x
1 - sin ² x
--------------------
sin x - 1/sin x
sin x ( 1 - sin ² x )
--------------------------
sin ² x - 1
- ( sin ² x - 1 ) sin x
----------------------------
sin ² x - 1
- sin x 
%281+-+sin%5E2+%28x%29%29%2F%28sin+%28x%29+-+csc+%28x%29%29

cos%5E2+%28x%29%2F%28sin+x+-+1%2Fsin+x%29 -------------- Replacing 1+-+sin%5E2+%28x%29 with cos%5E2+%28x%29, and csc+%28x%29 with 1%2Fsin+%28x%29

cos%5E2+%28x%29%22%F7%22sin+x+-+1%2Fsin+x%29

cos%5E2+%28x%29%22%F7%22%28sin%5E2+%28x%29+-+1%29%2Fsin+x%29

cos%5E2+%28x%29%22%F7%22%28-+cos%5E2+%28x%29%29%2Fsin+x ------ Replacing sin%5E2+%28x%29+-+1 with -+cos%5E2+%28x%29

cos%5E2+%28x%29%22%2A%22-+sin+x%2Fcos%5E2+%28x%29

cross%28cos%5E2+%28x%29%29%22%2A%22-+sin+x%2Fcross%28cos%5E2+%28x%29%29_____highlight_green%28-+sin+x%29