Re: Rewriting of Trigonometric Functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg26835] Re: [mg26803] Rewriting of Trigonometric Functions*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Thu, 25 Jan 2001 01:13:15 -0500 (EST)*References*: <200101240918.EAA03580@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Thomas Engelhardt wrote: > > Dear Mathgroup members, > > I have just started to use Mathematica and directly ran into a problem: > > I have rather lengthy expressions resulting from putting a sum of two > sinusodial swings to the power of three (Two-tone Intermodulation). > In order for me to recognise the contained frequencies I want Mathematica to > rewrite the contained Trigonometric functions in certain ways, namely like: > > [sin(a)]^2 should be transformed into 1/2*(1+cos2x) > and for higher powers accordingly. > > Furthermore: > sin(a)*sin(b) should be changed to 1/2*[cos(a-b) - cos(a+b)] > > I have tried all kinds of "Expand" and "Trig..." operations but Mathematica > always keeps the powers on the trigonometric functions and doesn't change > the multiplications either. > > Does anybody have an idea how I can get Mathematica to transform the > expressions in the desired way? > > I appreciate your help! > Thanks in advance. > > Kind Regards > > Thomas > Munich, Germany In[9]:= Sin[a]*Sin[b] // TrigReduce // InputForm Out[9]//InputForm= (Cos[a - b] - Cos[a + b])/2 In[10]:= Sin[a]^2 // TrigReduce // InputForm Out[10]//InputForm= (1 - Cos[2*a])/2 Daniel Lichtblau Wolfram Research

**References**:**Rewriting of Trigonometric Functions***From:*thomas-a.engelhardt@t-online.de (Thomas Engelhardt)