document.write( "Question 951508: Find all solutions, showing the work, of the equation on [0,2π].
\n" ); document.write( "1 = cot^2 + csc x \n" ); document.write( "

Algebra.Com's Answer #581203 by lwsshak3(11628) $\"\"$ $\"About$

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Find all solutions, showing the work, of the equation on [0,2π].
\n" ); document.write( "1 = cot^2 + csc x
\n" ); document.write( " $\"1=cot%5E2%28x%29%2Bcscx\"$
\n" ); document.write( " $\"1=cos%5E2%28x%29%2Fsin%5E2%28x%29%2B1%2Fsinx\"$
\n" ); document.write( "lcd:sin^2(x)
\n" ); document.write( " $\"sin%5E2%28x%29=%28cos%5E2%28x%29%2Bsinx%29\"$
\n" ); document.write( " $\"sin%5E2%28x%29=1-sin%5E2%28x%29%2Bsinx\"$
\n" ); document.write( "2sin^2(x)-sinx-1+0
\n" ); document.write( "(2sinx+1)(sinx-1)=0
\n" ); document.write( "..
\n" ); document.write( "2sinx+1=0
\n" ); document.write( "sinx=-1/2
\n" ); document.write( "x=π/6,11π/6
\n" ); document.write( "or
\n" ); document.write( "sinx-1=0
\n" ); document.write( "x=0,π,2π\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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