document.write( "Question 77181: if tanA + secA = 2 where a is acute then which option is correct.\r
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Algebra.Com's Answer #55314 by Edwin McCravy(20063)\"\" \"About 
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document.write( "if tanA + secA = 2 where a is acute then which option is correct. \r\n" );
document.write( "a) tan A < Sec A\r\n" );
document.write( "b) Cosec A > CotA\r\n" );
document.write( "c) Sec A > Cosec A\r\n" );
document.write( "d) CotA > Tan A\r\n" );
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document.write( "Your teacher made a mistake in asking \r\n" );
document.write( "\"which option is correct\"? He or she should\r\n" );
document.write( "have asked \"Which option is INcorrect?\"\r\n" );
document.write( "because it turns out that c) is the only \r\n" );
document.write( "INcorrect one!!\r\n" );
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document.write( "Put tanA + secA = 2 with the trig identity\r\n" );
document.write( "1 + tan²A = sec²A\r\n" );
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document.write( "and we have the system of equations\r\n" );
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document.write( "tanA + secA = 2\r\n" );
document.write( "  1 + tan²A = sec²A\r\n" );
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document.write( "Solve by substitution:\r\n" );
document.write( "Solve the first for secA\r\n" );
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document.write( "       secA = 2 - tanA\r\n" );
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document.write( "Substitute into the second equation\r\n" );
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document.write( "  1 + tan²A = (2 - tanA)²\r\n" );
document.write( "  1 + tan²A = 4 - 4tanA + tan²A\r\n" );
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document.write( "The tan²A's cancel and we get\r\n" );
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document.write( "          1 = 4 - 4tanA\r\n" );
document.write( "      4tanA = 3\r\n" );
document.write( "      tan A = 3/4\r\n" );
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document.write( "So we can draw a right triangle ABC \r\n" );
document.write( "containing angle A with 3 as A's \r\n" );
document.write( "opposite side and 4 as A's adjacent\r\n" );
document.write( "side:\r\n" );
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document.write( "           B  \r\n" );
document.write( "         . |\r\n" );
document.write( "     .     |3 \r\n" );
document.write( "A._________|\r\n" );
document.write( "     4      C\r\n" );
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document.write( "We can calculate the hypotenuse by the \r\n" );
document.write( "Pythagorean theorem.\r\n" );
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document.write( "c² = a² + b²\r\n" );
document.write( "c² = 3² + 4²\r\n" );
document.write( "c² = 9 + 16\r\n" );
document.write( "c² = 25\r\n" );
document.write( "c = 5\r\n" );
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document.write( "So the triangle has hypotenuse c = AB = 5\r\n" );
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document.write( "           B  \r\n" );
document.write( "         . |\r\n" );
document.write( "    5.     |3 \r\n" );
document.write( "A._________|\r\n" );
document.write( "     4      C\r\n" );
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document.write( "Now we check the choices:             \r\n" );
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document.write( "a) tan A < Sec A\r\n" );
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document.write( "   3/4 < 5/4   yes that's true \r\n" );
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document.write( "b) Cosec A > CotA\r\n" );
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document.write( "    5/3 > 4/3  yes that's true\r\n" );
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document.write( "c) Sec A > Cosec A\r\n" );
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document.write( "    5/4 > 5/3  no that's false\r\n" );
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document.write( "d) CotA > Tan A\r\n" );
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document.write( "    4/3 > 3/4 yes that's true.\r\n" );
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document.write( "They are all true but c)!!\r\n" );
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document.write( "Edwin

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