ATAR Notes: Forum

HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Extension 1 => Topic started by: catda on July 16, 2019, 12:03:58 pm

Title: need help
Post by: catda on July 16, 2019, 12:03:58 pm

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

Title: Re: need help
Post by: RuiAce on July 16, 2019, 01:42:13 pm

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