document.write( "Question 807741: cot(sec^-1(x)) \n" ); document.write( "
Algebra.Com's Answer #486492 by Edwin McCravy(20054)\"\" \"About 
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document.write( "cot(sec-1(x))\r\n" );
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document.write( "Inside the parentheses is sec-1(x).  That says\r\n" );
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document.write( "\"The angle whose secant is x.  Let that angle = q.\r\n" );
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document.write( "So we draw a right triangle including the angle q = sec-1(x).\r\n" );
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document.write( "Now to make sure that this angle is the angle whose secant is x,\r\n" );
document.write( "We do the following:\r\n" );
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document.write( "1. We note that the secant is the hypotenuse over the adjacent. \r\n" );
document.write( "2. We notice that x is equivalent to \"x%2F1\".\r\n" );
document.write( "3. We label the hypotenuse as the numerator x.\r\n" );
document.write( "4. We label the adjacent side to q as the denominator 1.\r\n" );
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document.write( "  \r\n" );
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document.write( "Next we use the Pythagorean theorem to find the opposite side:\r\n" );
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document.write( "   c² = a² + b²\r\n" );
document.write( "   x² = 1² + b²\r\n" );
document.write( "   x² = 1 + b²\r\n" );
document.write( " x²-1 = b²\r\n" );
document.write( "√x²-1 = b\r\n" );
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document.write( "So we label the opposite side as √x²-1\r\n" );
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document.write( "Now we go back to the original problem:\r\n" );
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document.write( "cot(sec-1(x)), that's the cot(q)\r\n" );
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document.write( "We want the cotangent of that angle.  We know that the cotangent is\r\n" );
document.write( "the adjacent over the opposite.   The adjacent is 1 and the opposite is \r\n" );
document.write( "√x²-1, so:\r\n" );
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document.write( "Answer: cot(sec-1(x)) = \"1%2Fsqrt%28x%5E2-1%29\".\r\n" );
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document.write( "Edwin
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