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August 21, 2019, 06:24:05 am

Author Topic: need help  (Read 72 times)  Share 

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catda

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need help
« on: July 16, 2019, 12:03:58 pm »
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Hi,
I need help with this question.
Simplfy sin(a+b)cosa-cos(a+b)sina

RuiAce

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Re: need help
« Reply #1 on: July 16, 2019, 01:42:13 pm »
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\[ \text{Temporarily, let us substitute }c = a+b\\ \text{Then }\sin(a+b)\cos a -\cos(a+b)\sin a = \sin c \cos a - \cos c \sin a \]
\[ \text{Now use your formula sheet. This is just equal to }\sin (c-a).\\ \text{At this point, we can then sub }c=a+b\text{ back in}\\ \text{to get }\sin [(a+b)-a]\text{, which simplifies to }\boxed{\sin b} \]