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need help

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catda:
Hi,
I need help with this question.
Simplfy sin(a+b)cosa-cos(a+b)sina

RuiAce:
\[ \text{Temporarily, let us substitute }c = a+b\\ \text{Then }\sin(a+b)\cos a -\cos(a+b)\sin a = \sin c \cos a - \cos c \sin a \]
\[ \text{Now use your formula sheet. This is just equal to }\sin (c-a).\\ \text{At this point, we can then sub }c=a+b\text{ back in}\\ \text{to get }\sin [(a+b)-a]\text{, which simplifies to }\boxed{\sin b} \]

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