document.write( "Question 1007411: Please help me solve this equation. I have a huge trig test tomorrow and I have no idea what I am doing... csc^2(2x)-csc(2x)=2 \n" ); document.write( "

Algebra.Com's Answer #623336 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Introduce new variable y = csc(2x).\r\n" );
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document.write( "Then your equation takes the form \r\n" );
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document.write( " = .\r\n" );
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document.write( "Factor it:\r\n" );
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document.write( "(y+1)*(y-2) = 0\r\n" );
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document.write( "The solutions are y = -1 and y = 2.\r\n" );
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document.write( "Now you need to solve two equations:\r\n" );
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document.write( "1) csc(2x) = -1 ----->  = -1 -----> sin(2x) = -1 -----> 2x = 270° -----> x = 135°.\r\n" );
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document.write( "2) csc(2x) = 2 ----->  = 2 -----> sin(2x) =  -----> 2x = 30° and 2x = 150° -----> x = 15° and x = 75°.\r\n" );
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document.write( "Answer. The solutions are x = 15°, x = 75° and x = 135°.\r\n" );
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