document.write( "Question 1159951: Solve: cos(x) cos (6x) =-1 \n" ); document.write( "

Algebra.Com's Answer #783091 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( " $\"cos%28x%29+cos+%286x%29+=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "-> you know that $\"-1%3C=cos%28x%29%3C=1\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "case 1: when $\"cos%28x%29=-1\"$ and $\"cos%286x%29+=1\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"cos%28x%29=-1\"$
\n" ); document.write( " $\"x=cos%5E-1%28-1%29\"$
\n" ); document.write( " $\"x=2pi%2An%2Bpi\"$ \r
\n" ); document.write( "\n" ); document.write( "and $\"cos+%286x%29+=1\"$
\n" ); document.write( "general solutions for $\"cos+%286x+%29=1\"$ is:
\n" ); document.write( " $\"6x=2pi%2An\"$
\n" ); document.write( " $\"x=%282pi%2An%29%2F6+\"$
\n" ); document.write( " $\"x=%28pi%2An%29%2F3\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "check: if $\"n=1\"$
\n" ); document.write( " $\"x=2pi%2Bpi=3pi\"$ ... for $\"cos%28x%29\"$
\n" ); document.write( " $\"x=pi%2F3\"$ ... for $\"cos+%286x+%29\"$
\n" ); document.write( " $\"cos%283pi%29%2Acos%286%28pi%2F3%29%29+=-1\"$ -> $\"true\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "case 2: when $\"cos%28x%29=1\"$ and $\"cos%286x%29+=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cos%28x%29=1\"$
\n" ); document.write( " $\"x=cos%5E-1%281%29\"$
\n" ); document.write( " $\"x=2pi%2An\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cos%286x%29+=-1\"$
\n" ); document.write( " $\"6x=2pi%2An%2Bpi\"$
\n" ); document.write( " $\"x=2pi%2An%2F6+%2Bpi%2F6\"$
\n" ); document.write( " $\"x=%28pi%2An%29%2F3%2Bpi%2F6\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "check: if $\"n=1\"$
\n" ); document.write( " $\"x=2pi\"$ ...for $\"cos%28x%29\"$
\n" ); document.write( " $\"x=pi%2F3%2Bpi%2F6=pi%2F2\"$ ... for $\"cos%286x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cos%282pi%29%2Acos%286%28pi%2F2%29%29+=-1\"$ -> $\"true\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );