sin(x)^2

How to expand a function like sin(x)^2 to output 1/2*(1-cos(2*x))? I tried expand(sin(x)^2) but it returns the same.

Answer 1

[Star Strider]

Use the rewrite function:

syms x 
ys = sin(x)^2;
ye = rewrite(ys, 'exp')
yc = rewrite(expand(ye), 'cos')

p[roducing:

yc =
1/2 - cos(2*x)/2

[Eth]

Thanks.

[Star Strider]

As always, my pleasure.

Answer 2

[Hose Orlando]

how do i put this matrix into matlab

[Walter Roberson]

syms A B C
[sin(A)^2, sin(B)^2, sin(C)^2   
 cos... etc

Answer 3

[Carlos Guerrero García]

Perhaps the following lines will be useful:

syms x; % Establishing 'x' as a symbolic variable
combine(sin(x)^2,'sincos') % For the 1st (original) question

ans = 

combine(sin(x)^3,'sincos') % For the last question

ans = 

[John D'Errico]

Note that combine is a useful tool, but one we see mentioned here rarely. So...

help sym/combine

  combine  Combine terms of the same algebraic structure.
     combine(S)
       tries to rewrite products of powers in the expression S as a
       single power.
     combine(S, T)
       combines several calls to the target function T in the expression f
       to a single call.
       The target T is specified as one of the strings
       'atan', 'exp', 'gamma', 'log', 'sincos', 'sinhcosh'.
     combine(..., 'IgnoreAnalyticConstraints',VAL)
       controls the level of mathematical rigor to use on the analytical
       constraints while combining (branch cuts, division by zero, and so on).
       Here, VAL can be TRUE or  FALSE. If you use TRUE, then combine uses
       a set of mathematical rules, such as ln(a) + ln(b) = ln(a*b),
       that are not generally correct, but can give simpler results.
       The default is FALSE.
 
     Examples:
       combine(2^x * 3^x)  returns  6^x
       combine((2^x)^i)    returns  (2^x)^i
       combine((2^x)^i, 'IgnoreAnalyticConstraints', true)
                           returns  2^(x*i)
       combine(log(x) + log(y), 'log')
                           returns  log(x) + log(y)
       combine(log(x) + log(y), 'log', 'IgnoreAnalyticConstraints', true)
                           returns  log(x*y)
 
      See also sym/simplify, sym/expand, sym/factor

    Documentation for sym/combine
       doc sym/combine