document.write( "Question 814827: Verify the identity. 1/1-cos + 1/1+cos = 2 Csc^2 \n" ); document.write( "
Algebra.Com's Answer #490554 by DrBeeee(684)\"\" \"About 
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Given;
\n" ); document.write( "(1) \"1%2F%281-cosx%29+%2B+1%2F%281%2Bcosx%29+=+2csc%5E2%28x%29\"
\n" ); document.write( "First combine the fractions on the left side of (1) by cross multiplying to get
\n" ); document.write( "(2)
\n" ); document.write( "Now add the numerator terms and multiply the denominator factors of the left side of (2) to get
\n" ); document.write( "(3) \"%281%2B1%2Bcosx-cosx%29%2F%281%2Bcosx-cosx-cos%5E2%28x%29%29+=+2csc%5E2%28x%29\" or
\n" ); document.write( "(4)\"%282%29%2F%281-cos%5E2%28x%29%29+=+2csc%5E2%28x%29\"
\n" ); document.write( "Now use the identity
\n" ); document.write( "(5) \"sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1\" to get
\n" ); document.write( "(6) \"sin%5E2%28x%29+=+1+-+cos%5E2%28x%29\"
\n" ); document.write( "Now substitute (6) into (4) to get
\n" ); document.write( "(7)\"%282%29%2F%28sin%5E2%28x%29%29+=+2csc%5E2%28x%29\"
\n" ); document.write( "Now use the reciprocal identity
\n" ); document.write( "(8)\"1%2F%28sin%28x%29%29+=+csc%28x%29\" to get
\n" ); document.write( "(9)\"1%2F%28sin%5E2%28x%29%29+=+csc%5E2%28x%29\" or
\n" ); document.write( "by multiplying both sides of (9) by 2 we get
\n" ); document.write( "(10) \"2%2F%28sin%5E2%28x%29%29+=+2csc%5E2%28x%29\"
\n" ); document.write( "Now substitute (10) into (7) to get
\n" ); document.write( "(11) \"2csc%5E2%28x%29+=+2csc%5E2%28x%29\" Q.E.D.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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