document.write( "Question 445499: find all solutions on the interval 0 ≤x≤2pi : sin^(2)x-3cos^(2)x=0 \n" ); document.write( "

Algebra.Com's Answer #306919 by Gogonati(855) $\"\"$ $\"About$

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$\"%28sinx%292-3%28cosx%29%5E2=0\"$ , substitute $\"%28sinx%29%5E2=1-%28cosx%29%5E2\"$ , and get:\r
\n" ); document.write( "\n" ); document.write( " $\"1-%28cosx%29%5E2-3%28cosx%29%5E2=0\"$ => $\"4%28cosx%29%5E2=1\"$ => $\"%28cosx%29%5E2=1%2F4\"$ . \r
\n" ); document.write( "\n" ); document.write( "The last equation is equivalent with two equations:\r
\n" ); document.write( "\n" ); document.write( " $\"cosx=1%2F2\"$ and $\"cosx=-1%2F2\"$ . The solution for the first equation is:\r
\n" ); document.write( "\n" ); document.write( " $\"x=pi%2F3\"$ and $\"x=5pi%2F3\"$ . The solution for the second equation is:\r
\n" ); document.write( "\n" ); document.write( " $\"x=2pi%2F3\"$ and $\"x=4pi%2F3\"$ .\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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