SOLUTION: sin(a+b)-sin(a-b)=2cosasinb How do I solve this problem? I am so close to a break down over this. Help!!

Question 408715: sin(a+b)-sin(a-b)=2cosasinb
How do I solve this problem? I am so close to a break down over this. Help!!

Found 3 solutions by robertb, jim_thompson5910, richard1234:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
The left-hand side reduces to sina*cosb + cosa*sinb - sina*cosb + cosa*sinb = 2cosa*sinb. Hence the equation is an identity, and all values for a , b are solutions.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
sin(a+b)-sin(a-b)=2cos(a)sin(b)

sin(a)cos(b)+cos(a)sin(b)-(sin(a)cos(b)-cos(a)sin(b))=2cos(a)sin(b)

sin(a)cos(b)+cos(a)sin(b)-sin(a)cos(b)+cos(a)sin(b)=2cos(a)sin(b)

(sin(a)cos(b)-sin(a)cos(b))+(cos(a)sin(b)+cos(a)sin(b))=2cos(a)sin(b)

0+2cos(a)sin(b)=2cos(a)sin(b)

2cos(a)sin(b)=2cos(a)sin(b)

So the original equation is an identity (ie it's true for ALL values of 'a' and 'b')

If you need more help, email me at jim_thompson5910@hotmail.com

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Jim
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
. The terms cancel out, so our expression is equal to which is the RHS, so we're done.
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