document.write( "Question 78521: let cos A= 1/5^(1/2) with A in Q 4. find tan 2A \n" ); document.write( "
Algebra.Com's Answer #56304 by Edwin McCravy(20077)\"\" \"About 
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document.write( "let cos(A)= 1/5^(1/2) with A in Q 4. find tan(2A)\r\n" );
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document.write( "------------------------\r\n" );
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document.write( "The 1/2 power is the same as the square root, so\r\n" );
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document.write( "cos(A) = 1/Ö5\r\n" );
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document.write( "The formula for tan(2A) is\r\n" );
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document.write( "            2·tan(A)\r\n" );
document.write( "tan(2A) = -------------\r\n" );
document.write( "           1 - tan²(A)\r\n" );
document.write( "                                           sin(A) \r\n" );
document.write( "so we need tan(A).  We know that tan(A) = -------- \r\n" );
document.write( "                                           cos(A)\r\n" );
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document.write( "and we have cos(A), so we need to get sin(A).\r\n" );
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document.write( "We know that sin²(A) = 1 - cos²(A), so substituting\r\n" );
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document.write( "1/Ö5 for cos(A),\r\n" );
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document.write( "sin²(A) = 1 - (1/Ö5)² = 1 - 1/5 = 4/5\r\n" );
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document.write( "Taking square roots:\r\n" );
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document.write( "sin(A) = ±Ö(4/5) = ± 2/Ö5\r\n" );
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document.write( "Since we know that A is in Q 4, and since the\r\n" );
document.write( "sine is negative in the 4th quadrant,\r\n" );
document.write( "we must take the negative sign, so\r\n" );
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document.write( "sin(A) = -2/Ö5              _\r\n" );
document.write( "             sin(A)     -2/Ö5      \r\n" );
document.write( "So tan(A) = -------- = -------- \r\n" );
document.write( "             cos(A)      1/Ö5        \r\n" );
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document.write( "Multiply top and bottom by Ö5 and you get:\r\n" );
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document.write( "tan(A) = -2\r\n" );
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document.write( "Now we plug that in:\r\n" );
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document.write( "            2·tan(A)         2(-2)         -4      -4      4\r\n" );
document.write( "tan(2A) = ------------- = ----------- = ------- = ----- = ---\r\n" );
document.write( "           1 - tan²(A)     1 - (-2)²     1 - 4     -3      3\r\n" );
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document.write( "Edwin

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