SOLUTION: Verify the identity: sin(a-b)- sin (a+b) - sin^2 b - cos^2 a = (sin b -cos a)^2 I am not sure which formulas to use to verify this. I was thinking the sun and difference formula

Algebra ->  Trigonometry-basics -> SOLUTION: Verify the identity: sin(a-b)- sin (a+b) - sin^2 b - cos^2 a = (sin b -cos a)^2 I am not sure which formulas to use to verify this. I was thinking the sun and difference formula      Log On


   

Question 869068: Verify the identity: sin(a-b)- sin (a+b) - sin^2 b - cos^2 a = (sin b -cos a)^2
I am not sure which formulas to use to verify this. I was thinking the sun and difference formulas but it did not work out when i tried them.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Yes, those are the only ones you can use.
sin%28a-b%29=sin%28a%29cos%28b%29-cos%28a%29sin%28b%29
sin%28a%2Bb%29=sin%28a%29cos%28b%29%2Bcos%28a%29sin%28b%29
So,

sin%28a-b%29-sin%28a%2Bb%29=-2cos%28a%29sin%28b%29
Then,


sin%28a-b%29-sin%28a%2Bb%29-sin%5E2%28b%29-cos%5E2%28a%29=-%28cos%28a%29%2Bsin%28b%29%29%5E2
So now this can't equal the right hand side %28sin%28b%29-cos%28a%29%29%5E2
Check the problem setup and make sure it's correct.