document.write( "Question 769455: Find all solutions in the interval [0, 2π). \r
\n" ); document.write( "\n" ); document.write( "sin2x - cos2x = 0 \n" ); document.write( "

Algebra.Com's Answer #468859 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+sin%28+2x+%29+-+cos%28+2x+%29+=+0+\"$
\n" ); document.write( " $\"+sin%28+2x+%29+=+cos%28+2x+%29+\"$
\n" ); document.write( "The sin and cos are equal when:
\n" ); document.write( " $\"+2x+=+pi%2F4+\"$
\n" ); document.write( " $\"+2x+=+%28+5%2Api+%29%2F4+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "At an angle of $\"+pi%2F4+\"$ ,
\n" ); document.write( " $\"+sin%28+pi%2F4+%29+=+1%2Fsqrt%282%29+\"$
\n" ); document.write( " $\"+cos%28+pi%2F4+%29+=+1%2Fsqrt%282%29+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+sin%28+5%2Api%2F4+%29+=+%28-1%29%2Fsqrt%282%29+\"$
\n" ); document.write( " $\"+cos%28+5%2Api%2F4+%29+=+%28-1%29%2Fsqrt%282%29+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "So, if I say
\n" ); document.write( " $\"+2x+=+pi%2F4+\"$
\n" ); document.write( " $\"+x+=+pi%2F8+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+2x+=+%28+5%2Api+%29%2F4+\"$
\n" ); document.write( " $\"+x+=+%28+5%2Api+%29+%2F+8+\"$
\n" ); document.write( "------------------
\n" ); document.write( "Solutions for $\"+x+\"$ are between ( 0, 2pi ), so
\n" ); document.write( " $\"+2x+=+2%2Api+%2B+pi%2F4+\"$
\n" ); document.write( " $\"+2x+=+2%2Api+%2B+%285pi%29%2F4+\"$
\n" ); document.write( "are solutions also\r
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