document.write( "Question 534177: find all the solutions on the interval [0,2pi)
\n" ); document.write( "2cot^2x+3cscx=0 \n" ); document.write( "

Algebra.Com's Answer #351415 by lwsshak3(11628) $\"\"$ $\"About$

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find all the solutions on the interval [0,2pi)
\n" ); document.write( "2cot^2x+3cscx=0
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\n" ); document.write( "2(cos^2x/sin^2x)+3(1/sinx)=0
\n" ); document.write( "(2cos^2x/sin^2x)+(3/sinx)=0
\n" ); document.write( "LCD: sin^2x
\n" ); document.write( "(2cos^2x)+(3sinx)=0
\n" ); document.write( "2(1-sin^2x)+3sinx=0
\n" ); document.write( "2-2sin^2x+3sinx=0
\n" ); document.write( "2sin^2x-3sinx-2=0
\n" ); document.write( "(2sinx+1)(sinx-2)=0
\n" ); document.write( "..
\n" ); document.write( "2sinx=1=0
\n" ); document.write( "sinx=-1/2
\n" ); document.write( "x=arcsin(-1/2)=7π/6 and 11π/6 (in quadrants III and IV where sin<0)
\n" ); document.write( "..
\n" ); document.write( "sinx-2=0
\n" ); document.write( "sinx≠2 (reject, (-1≤sinx≤1)
\n" ); document.write( "solutions:7π/6 and 11π/6 \n" ); document.write( "

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