
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 31st, 2017, 12:16 PM  #1 
Senior Member Joined: Apr 2008 Posts: 162 Thanks: 3  simplify without double angle identities
I am going to write down a math problem below. (ex) Without using double angle identities, simplify 2cos(3x)*sinx my attempt: 2cos(3x)*sinx =2cos(x+2x)*sinx =2sinx*cosx*cos(2x)2sinx*sinx*sin(2x) =2sinx*cosx*cos(2x)2(sinx)^2*sin(2x) =2sinx*cosx*(cosx*cosxsinx*sinx)2sin(2x)+2(cosx)^2*sin(2x) =2sinx*(cosx)^32(sinx)^3*cosx2sin(2x)+2(cosx)^2*sin(2x) My strategy makes the original expression very messy. I am really stuck. The answer is sin(4x)sin(2x). Can someone explain how to do the problem without double angle identities? Thanks a lot. 
January 31st, 2017, 01:27 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,407 Thanks: 859 Math Focus: Elementary mathematics and beyond 
$$2\cos(3x)\sin(x)=\sin(3x+x)\sin(3xx)=\sin(4x)\sin(2x)$$

January 31st, 2017, 02:52 PM  #3 
Senior Member Joined: Apr 2008 Posts: 162 Thanks: 3 
Thanks. greg1313. There is something I don't get. What made you use sin(3x+x)  sin(3xx)? This is not obvious to me.

January 31st, 2017, 04:26 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,407 Thanks: 859 Math Focus: Elementary mathematics and beyond 
The problem you posted is a specific case of a well known identity.

January 31st, 2017, 07:02 PM  #5 
Member Joined: Oct 2016 From: Melbourne Posts: 77 Thanks: 35  
January 31st, 2017, 11:57 PM  #6 
Senior Member Joined: Apr 2008 Posts: 162 Thanks: 3 
Because I didn't know anything about this wellknown identity, I had a hard time with the problem. How would you approach it if you didn't know that identity?

February 1st, 2017, 02:08 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 16,595 Thanks: 1199 
Alternatively, use $\cos(\theta) = (e^{i\theta} + e^{i\theta})/2$, $\sin(\theta) = (e^{i\theta}  e^{i\theta})/(2i)$, and the law of exponents. The task then reduces to easy algebra.

February 2nd, 2017, 10:27 PM  #8 
Senior Member Joined: Apr 2008 Posts: 162 Thanks: 3 
This problem "looks" easy, but it requires you to use advanced ideas to solve it like the polar form of sine and cosine. I wish there was a much easier way to do it. Thanks, everyone. 

Tags 
angle, double, identities, simplify 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
simplify using trig identities  unistu  Trigonometry  9  February 4th, 2015 09:51 PM 
Help with Double Angle Identities!!!  whittwhitt  Algebra  3  November 27th, 2012 06:31 PM 
Multiple Angle Identities  SophieG  Algebra  13  September 16th, 2011 02:24 PM 
Double angle formulae  hoyy1kolko  Algebra  1  May 5th, 2011 06:54 AM 
Angle identities question?  Summer  Algebra  1  January 19th, 2008 03:56 PM 