document.write( "Question 1024326: Write the given expression in terms of x and y only! \r
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Algebra.Com's Answer #639805 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I think the lady above made a careless error and \r\n" );
document.write( "also did not take the four cases of signs of sines and\r\n" );
document.write( "cosines in the various quadrants.\r\n" );
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document.write( "sin(sin-1x + cos-1y)\r\n" );
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document.write( "Let A = sin-1x  then sinA = x\r\n" );
document.write( "Let B = cos-1y  then cosB = y\r\n" );
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document.write( "and B = cos-1x\r\n" );
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document.write( "sin(A + B) = sinA∙cosB + cosA∙sinB\r\n" );
document.write( "           = x∙y + cosA∙sinB\r\n" );
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document.write( "There are four cases.\r\n" );
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document.write( "1. sin-1x is non-negative and cos-1x is non-negative.\r\n" );
document.write( "2. sin-1x is non-negative and cos-1x is negative.\r\n" );
document.write( "3. sin-1x is negative and cos-1x is non-negative.\r\n" );
document.write( "4. sin-1x is non-negative and cos-1x is non-negative.\r\n" );
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document.write( "But in all cases, since \r\n" );
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document.write( "cosA = ±√1-sin²A = ±√1-x²±\r\n" );
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document.write( "sinB = ±√1-cos²B = ±√1-y²\r\n" );
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document.write( "sin(A + B) = xy ± √(1-x²)(1-y²) \r\n" );
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document.write( "Edwin
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