document.write( "Question 1113541: For cosxcos3x−sinxsin3x=0, use an addition or subtraction formula to simplify the equation and then find all four solutions of the equation in the interval [0,π). \n" ); document.write( "

Algebra.Com's Answer #728601 by ikleyn(52817) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Use the addition formula for cosine  cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In your case, a = x, b = 3x, and the left side of your equation is cos(x+3x) = cos(4x).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus your equation takes the form\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "cos(4x) = 0,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which implies  4x = , ,  ,  ,  . . . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence,  x = ,  ,  ,  ,  and the rest of the roots are out of the given interval.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The solutions of the given equation in the given interval are x= ,  ,  ,  .\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "---------------
\n" ); document.write( "On solving trigonometric equations, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solving simple problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving typical problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving more complicated problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving advanced problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );