document.write( "Question 1167173: Question: TanA = v; A is in Quadrant 1. Obtain Sin2A and Cos2A.\r
\n" ); document.write( "\n" ); document.write( "My work so far: Assume the hypotenuse as 1, designate the sides X and Y (corresponding to axis). And I can get appropriate ansers based on the formula in abstract form. \r
\n" ); document.write( "\n" ); document.write( "But I have no idea as to how to approach the problem to come to answers given in the book as Sin2A = 2v/(1+v^2) and Cos2A = (1 - v^2)/(1+v^2)\r
\n" ); document.write( "\n" ); document.write( "Do I disignae Hypotenuse as v and the sides 1 and 2?
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\n" ); document.write( "\n" ); document.write( "Please help. Or if this question is already solved and posted on this site, just give me the question number and I can look it up.
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Algebra.Com's Answer #791856 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I think you are to draw an isosceles triangle and use the law of sines and the\r\n" );
document.write( "law of cosines on it.\r\n" );
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document.write( "Since A is in Quadrant I, it is acute.  So we draw an isosceles triangle with\r\n" );
document.write( "each base angle equal to A, and the perpendicular bisector of the base, which\r\n" );
document.write( "we let be v, and each half of the base be 1.  Then the vertex angle (angle at\r\n" );
document.write( "the top) will be 180°-2A and the base equal to 2, like this. Then, since the\r\n" );
document.write( "isosceles triangle is split into two congruent right triangles, by the\r\n" );
document.write( "Pythagorean theorem, each leg of the isosceles triangle is √(1+v²)\r\n" );
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document.write( "By the law of sines, the ratio of the length of a side of a triangle to the\r\n" );
document.write( "sine of the angle opposite that side is the same for all sides and angles in\r\n" );
document.write( "any triangle, so for the whole isosceles triangle with base 2,\r\n" );
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document.write( ".  That's because the sine of an angle is equal to\r\n" );
document.write( "the sine of its supplement. So, \r\n" );
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document.write( ", and therefore\r\n" );
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document.write( "Cross-multiply,\r\n" );
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document.write( "From the right triangle on the left, sin(A)=opposite/hypotenuse,\r\n" );
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document.write( "Multiply both sides by √(1+v^2)\r\n" );
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document.write( "Divide both sides by 1+v²\r\n" );
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document.write( "Next we use the law of cosines with the same triangle above:\r\n" );
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document.write( "The square of a side of a triangle is equal to the sum of the squares of the\r\n" );
document.write( "other two sides minus twice the product of the other two sides multiplied by\r\n" );
document.write( "the cosine of the angle between them.\r\n" );
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document.write( ".  That's because the cosine of an angle is equal\r\n" );
document.write( "to the negative of the cosine of its supplement. So we simplify and substitute\r\n" );
document.write( "-cos(2A) for cos(180°-2A)\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "Solve for cos(2A)\r\n" );
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document.write( "Edwin

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