document.write( "Question 307231: This is a Trigonometric Identity Problem.\r
\n" ); document.write( "\n" ); document.write( "Simplify the expression: csc(-x)-csc(-x)cos^2(x)\r
\n" ); document.write( "\n" ); document.write( "I think that the two csc(-x)s cancel out to leave the answer being cos^2(x) but I'm not sure since they are multiplied.\r
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Algebra.Com's Answer #219827 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Rules for trig functions of negative values:\r\n" );
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document.write( "The cosine and secant are the only even trig functions,\r\n" );
document.write( "and the negative sign \"disappears\":\r\n" );
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document.write( "\"cos%28-theta%29+=+cos%28theta%29\"\r\n" );
document.write( "\"sec%28-theta%29+=+sec%28theta%29\"\r\n" );
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document.write( "All the other trig functions are odd trig functions,\r\n" );
document.write( "and the negative sign comes out in front:\r\n" );
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document.write( "\"sin%28-theta%29+=+-sin%28theta%29\"\r\n" );
document.write( "\"tan%28-theta%29+=+-tan%28theta%29\"\r\n" );
document.write( "\"csc%28-theta%29+=+-csc%28theta%29\"\r\n" );
document.write( "\"cot%28-theta%29+=+-cot%28theta%29\"\r\n" );
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document.write( "csc(-x)-csc(-x)cos2(x) becomes\r\n" );
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document.write( "-csc(x)-[-csc(x)]cos2(x) \r\n" );
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document.write( "-csc(x)+csc(x)cos2(x)\r\n" );
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document.write( "Factor out -csc(x)\r\n" );
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document.write( "-csc(x)[1-cos2(x)]\r\n" );
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document.write( "Us the identity \"Sin%5E2theta%2BCos%5E2theta=1\" written as \"Sin%5E2theta=1-Cos%5E2theta\" to replace the bracketed expression:\r\n" );
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document.write( "-csc(x)sin2(x)\r\n" );
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document.write( "Use the identity \"csc%28theta%29=1%2Fsin%28theta%29\" to replace the cosecant factor:\r\n" );
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document.write( "-\"1%2Fsin%28x%29\"sin2(x)\r\n" );
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document.write( "This simplifies to\r\n" );
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document.write( "-sin(x)\r\n" );
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document.write( "Edwin

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