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May 24th, 2009, 06:55 PM  #1 
Newbie Joined: May 2009 Posts: 3 Thanks: 0  Proof of a law of cosine/sine
Can you help me prove sin 3A = 3 sin A cos^2 A  sin^3 A or (cos A + i sin A)^3 = cos 3A + i sin 3A? Last edited by skipjack; February 28th, 2018 at 01:25 PM. 
May 25th, 2009, 03:35 AM  #2  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Proof of a law of cosine/sine Quote:
Have you learned the power reduction formula $\displaystyle \sin^3{A}=\frac{3\sin{A}\sin{3A}}{4}$? Quote:
Last edited by skipjack; February 28th, 2018 at 01:23 PM.  
May 25th, 2009, 07:31 AM  #3 
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: Proof of a law of cosine/sine
Depending on your classroom procedure, you can do the first by expansion formula [sin(A+B) = sinAcosB + cosAsinB] applied a couple of times. The second can be done by algebraic expansion, then using in part the first result.


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