document.write( "Question 438966: Prove the following is an identity.\r
\n" ); document.write( "\n" ); document.write( "1) 2csc^2 x = [(1/(1+cos x)] + [(1/1-cos x)]\r
\n" ); document.write( "\n" ); document.write( "2)cos x/(sin x*tan x+ cos x) = 1/ sec^2 x\r
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Algebra.Com's Answer #303461 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "             1             1\r\n" );
document.write( "2csc²x = —————————  +  —————————\r\n" );
document.write( "         1 + cos x     1 - cos x\r\n" );
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document.write( "The LCD on the right is (1 + cos x)(1 - cos x)\r\n" );
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document.write( "             1(1 - cos x)             1(1 + cos x)\r\n" );
document.write( "2csc²x = —————————————————————— +  —————————————————————— \r\n" );
document.write( "         (1 + cos x)(1 - cos x)    (1 - cos x)(1 + cos x)\r\n" );
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document.write( "              1 - cos x                 1 + cos x\r\n" );
document.write( "2csc²x = —————————————————————— +  —————————————————————— \r\n" );
document.write( "         (1 + cos x)(1 - cos x)    (1 - cos x)(1 + cos x)\r\n" );
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document.write( "Combine over the common denominator:\r\n" );
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document.write( "          1 - cos x  + 1 + cos x\r\n" );
document.write( "2csc²x = ————————————————————————  \r\n" );
document.write( "          (1 + cos x)(1 - cos x)   \r\n" );
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document.write( "Simplify the top and FOIL out the bottom\r\n" );
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document.write( "              2      \r\n" );
document.write( "2csc²x = ———————————  \r\n" );
document.write( "          1 - cos²x \r\n" );
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document.write( "Use the identity \"Sin%5E2theta+%2B+Cos%5E2theta+=+1\" written as \"Sin%5E2theta+=+1+-+Cos%5E2theta\" to \r\n" );
document.write( "rewrite the denominator:\r\n" );
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document.write( "            2      \r\n" );
document.write( "2csc²x = ———————  \r\n" );
document.write( "          sin²x\r\n" );
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document.write( "              1      \r\n" );
document.write( "2csc²x = 2*———————  \r\n" );
document.write( "            sin²x\r\n" );
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document.write( "Use the identity \"Csc%28theta%29+=+1%2F%28Sin%28theta%29%29\" with both sides squared\r\n" );
document.write( "which is \"Csc%5E2theta+=+1%2F%28Sin%5E2theta%29\" to rewrite the second\r\n" );
document.write( "factor on the right side:\r\n" );
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document.write( "2csc²x = 2csc²x \r\n" );
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document.write( "Edwin

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