document.write( "Question 671061: Assume
\n" ); document.write( "3 cos(x) − 4 sin(x) = 4\r
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\n" ); document.write( "4 cos(x) + 3 sin(x )= 3
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\n" ); document.write( "Find the exact (numeric) value of cot(x). \n" ); document.write( "

Algebra.Com's Answer #417258 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "3 cos(x) - 4 sin(x) = 4 \r\n" );
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document.write( "Divide through by sin(x)\r\n" );
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document.write( "3 - 4 = \r\n" );
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document.write( "3cot(x) - 4 = 4csc(x)\r\n" );
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document.write( "-------------------\r\n" );
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document.write( "4 cos(x) + 3 sin(x )= 3\r\n" );
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document.write( "Also divide through by sin(x)\r\n" );
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document.write( "4 + 3 = \r\n" );
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document.write( "4cot(x) + 3 = 3csc(x)\r\n" );
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document.write( "So we have the system:\r\n" );
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document.write( "3cot(x) - 4 = 4csc(x)\r\n" );
document.write( "4cot(x) + 3 = 3csc(x)\r\n" );
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document.write( "To eliminate the cosecant terms, multiply the first through \r\n" );
document.write( "by -3 and the second through by 4, and add them term by term:\r\n" );
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document.write( "-9cot(x) + 12 = -12csc(x)\r\n" );
document.write( "16cot(x) + 12 =  12csc(x)\r\n" );
document.write( "-------------------------\r\n" );
document.write( " 7cot(x) + 24 = 0\r\n" );
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document.write( "      7cot(x) = 24\r\n" );
document.write( "       cot(x) = \r\n" );
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document.write( "Edwin

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