Question 1208305
<pre>
{{{(sin(x)+i*cos(x)^"")^9}}}{{{""=""}}}{{{sin(9x)^""+i*cos(9x)^"")}}}

I think the teacher wanted it proved or disproved using the complement, 
given this:

{{{(cos(theta)+i*sin(theta)^"")^9}}}{{{""=""}}}{{{cos(9theta)+i*sin(9theta)}}}

{{{matrix(1,4,Let,theta,""="",pi/2-x)}}}

{{{(cos(pi/2-x)+i*sin(pi/2-x)^"")^9}}}{{{""=""}}}{{{cos(9(pi/2-x)^"")+i*sin(9(pi/2-x)^"")}}}

{{{(sin(x)+i*cos(x)^"")^9}}}{{{""=""}}}{{{cos(expr((9pi)/2)-9x)^""+i*sin(expr((9pi)/2)-9x)^"")}}}

{{{(sin(x)+i*cos(x)^"")^9}}}{{{""=""}}}{{{cos(4pi+expr((pi)/2)-9x)^""+i*sin(4pi+expr((pi)/2)-9x)^"")}}}

{{{(sin(x)+i*cos(x)^"")^9}}}{{{""=""}}}{{{cos(expr((pi)/2)-9x)^""+i*sin(expr((pi)/2)-9x)^"")}}}

{{{(sin(x)+i*cos(x)^"")^9}}}{{{""=""}}}{{{sin(9x)^""+i*cos(9x)^"")}}}

Proved, so true.

Edwin</pre>