SOLUTION: Complete the identity. A = Alpha. B = Beta Sin(A+B)cosB - cos(A+ B)sinB = sinAcos^2B+ sinAsin^2 B Please show me step by step on how to get them to look the same. Thanks.

Question 1067794: Complete the identity. A = Alpha. B = Beta
Sin(A+B)cosB - cos(A+ B)sinB = sinAcos^2B+ sinAsin^2 B
Please show me step by step on how to get them to look the same. Thanks.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
sin (a+b)=sin a cos b+ cos a*sin b==multiply by cos b====get sin a*cos b^2+cos a sin b cos b.
cos(a+b)=cos a cos b-sin a* sin b====multiply by sin b and change signs==-cos a cos b sin b+sin a sin^2 b
There are four terms and two cancel each other
sin a cos b^2+ sin a sin ^2 b.
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