I know and understand the formulas for sin(a+b), cos(a+b), etc. and how they're geometrically proven.
I tried to derive a formula for sin(a+b+c) just to begin with couldn't really get anywhere, can anyone attempt this problem and share a solution?
Asked
Active
Viewed 41 times
-1
-
Related (duplicate?): "Deriving multi-angle addition sin formulaes". See, in particular, this answer of mine. – Blue Aug 03 '22 at 15:49
-
Does this answer your question? Deriving multi-angle addition sin formulaes – Andrei Aug 03 '22 at 17:08
-
Does this answer your question? Evaluating $\cos(\alpha+\beta+\gamma)$ – Mateo Aug 03 '22 at 23:51
1 Answers
1
HINT
If $x = b+c$ then $$ \sin(a+b+c) = \sin(a+x) $$ and you can apply the usual sine expansion. When you are done, you will have the result in terms of $\sin(x)$ and $\cos(x)$, but $$ \sin(x) = \sin(b+c) $$ and you can apply the expansion again. Ditto with the cosine.
Please feel free to post results of your work below in comments or update your question for further guidance.
gt6989b
- 54,422