SOLUTION: 1+Sin(x) sin(x) - cos(x) + 1 ------- = ----------- ------- cos(X) sin(x) + cos(x) + 1 Verify the identity. I tried different ways , but still cannot get it.

Algebra ->  Trigonometry-basics -> SOLUTION: 1+Sin(x) sin(x) - cos(x) + 1 ------- = ----------- ------- cos(X) sin(x) + cos(x) + 1 Verify the identity. I tried different ways , but still cannot get it.      Log On


   

Question 1067735: 1+Sin(x) sin(x) - cos(x) + 1
------- = -------------------
cos(X) sin(x) + cos(x) + 1
Verify the identity.
I tried different ways , but still cannot get it. Please help.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52906) About Me  (Show Source):
You can put this solution on YOUR website!
.
It is NOT an identity.





Plot y = %281%2Bsin%28x%29%29%2Fcos%28x%29 (red, the left side) and y = %28sin%28x%29+-+cos%28x%29+%2B+1%29%2F%28sin%28x%29+%2B+cos%28x%29+%2B+1%29 (green, the right side)



Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Properly expressed on the site your identity to prove is

(1+sin(x))/cos(x)=(sin(x)-cos(x)+1)/(sin(x)+cos(x)+1)

and rendered should appear



Way, way, way too much text to try to put in here, but I tried starting with the right hand side,
and multiplied top and bottom by sin%28x%29-cos%28x%29-1, worked through some arithmetic, followed the difference of squares, did more steps...,

and came to sin%28x%29%2F%28cos%28x%29%2B1%29.

Not really finished, so still more work to do.