document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208305>Question 1208305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ((sin (x) + i cos (x)))^9 = sin (9 x) + i cos (9 x) ,   (true or false </SPAN>\n" );
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document.write( "Answer: <font color=red>True</font>\r<BR>\n" );
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document.write( "z = sin(x) + i*cos(x)<BR>\n" );
document.write( "z = cos(90-x) + i*sin(90-x) ......... use <a  rel=nofollow HREF=\"https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet_Reduced.pdf\">trig identities</a><BR>\n" );
document.write( "z^9 = cos(9*(90-x)) + i*sin(9*(90-x))   ................   <a  rel=nofollow HREF=\"https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/06%3A_The_Polar_System/6.05%3A_De_Moivre's_and_the_nth_Root_Theorem\">De Moivre's Theorem</a><BR>\n" );
document.write( "z^9 = cos(810 - 9x) + i*sin(810 - 9x)<BR>\n" );
document.write( "z^9 = cos(810)cos(9x) + sin(810)sin(9x) + i*( sin(810)cos(9x) - cos(810)sin(9x) ) .... use two more trig identities<BR>\n" );
document.write( "z^9 = 0*cos(9x) + 1*sin(9x) + i*( 1*cos(9x) - 0*sin(9x) )<BR>\n" );
document.write( "z^9 = sin(9x) + i*cos(9x)<BR>\n" );
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