How would you use the sum and difference identities to prove: 2sin(a+b)sin(a-b) = cos(2b) - cos(2a) ?

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Answer 1 · 2016-10-24T01:24:06

Let #a+b=x and a-b =y#

So #2a=x+y and 2b =x-y#

Now #RHS=cos2b-cos2a#

#=cos(x-y)-cos(x+y)#

#=cosxcosy+sinxsiny-cosxcosy+sinxsiny#

#=2sinxsiny#

#=2sin(a+b)sin(a-b)=LHS#