document.write( "Question 1078891: 2 acute angles, A and B are such that cot A = 7 and tan(A - B) = -1.
\n" ); document.write( "Without evaluating A and B,
\n" ); document.write( "i) show that tan B = 4/3,
\n" ); document.write( "ii) evaluate sin A and cos B,
\n" ); document.write( "iii) evaluate sin^2(2A) + cos^2(2B).
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Algebra.Com's Answer #693319 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hello,\r\n" );
document.write( "I have found that often when I do a hard problem like this for \r\n" );
document.write( "a student, the student often just turns in what I did and learns \r\n" );
document.write( "nothing.  So what I'm doing here is changing the numbers and \r\n" );
document.write( "doing a problem exactly like yours, that requires exactly the same \r\n" );
document.write( "steps from beginning to end.  So I'm doing this one instead of yours,\r\n" );
document.write( "which only has the numbers changed.  Use it as a model to do\r\n" );
document.write( "yours by, and you will learn something that way.  If you have\r\n" );
document.write( "any trouble, or don't understand something, just tell me in the\r\n" );
document.write( "thank-you note form below and I'll get back to you promptly by\r\n" );
document.write( "email.  No charge ever, as I do this for fun.
2 acute angles, A and B, are such that cot A = 12 and tan(A-B) = -2.
\n" ); document.write( "Without evaluating A and B,\r
\n" ); document.write( "\n" ); document.write( "i) show that tan B = 5/2,
\n" ); document.write( "ii) evaluate sin A and cos B,
\n" ); document.write( "iii) evaluate sin^2(2A) + cos^2(2B).
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document.write( "\"cot%28A%29+=+1%2Ftan%28A%29=12\" therefore \"tan%28A%29=1%2F12\"\r\n" );
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document.write( "\"tan%28A-B%29=%28tan%28A%29-tan%28B%29%29%2F%281%2Btan%28A%29tan%28B%29%29=-2\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28tan%28A%29-tan%28B%29%29%2F%281%2Btan%28A%29tan%28B%29%29=-2\"\r\n" );
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document.write( "\"tan%28A%29-tan%28B%29=-2%281%2Btan%28A%29tan%28B%29%29\"\r\n" );
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document.write( "\"tan%28A%29-tan%28B%29=-2-2tan%28A%29tan%28B%29%29\"\r\n" );
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document.write( "\"1%2F12-tan%28B%29=-2-2%281%2F12%29tan%28B%29\"\r\n" );
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document.write( "\"1%2F12-tan%28B%29=-2-%281%2F6%29tan%28B%29\"\r\n" );
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document.write( "Multiply thru by 12\r\n" );
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document.write( "\"1-12tan%28B%29=-24-2tan%28B%29\"\r\n" );
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document.write( "\"-10tan%28B%29=-25\"\r\n" );
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document.write( "\"tan%28B%29=%28-25%29%2F%28-10%29\"\r\n" );
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document.write( "\"tan%28B%29=5%2F2\"
ii) evaluate sin A and cos B,
\"cot%28A%29=12=12%2F1=adjacent%2F%28opposite%29\"\r\n" );
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document.write( "Draw a right triangle in QI that has angle A with adjacent=12\r\n" );
document.write( "and opposite=1. Using the Pythagorean theorem, the hypotenuse \r\n" );
document.write( "is \"sqrt%2812%5E2%2B1%5E2%29=sqrt%28144%2B1%29=sqrt%28145%29\". \r\n" );
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document.write( "So \"sin%28A%29=opposite%2F%28hypotenuse%29=1%2Fsqrt%28145%29=sqrt%28145%29%2F145\"\r\n" );
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document.write( "-------------------\r\n" );
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document.write( "\"tan%28B%29=5%2F2=opposite%2F%28adjacent%29\"\r\n" );
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document.write( "Draw a right triangle in QI that has angle B with opposite=5\r\n" );
document.write( "and adjacent=2. Using the Pythagorean theorem, the hypotenuse \r\n" );
document.write( "is \"sqrt%285%5E2%2B2%5E2%29=sqrt%2825%2B4%29=sqrt%2829%29\". \r\n" );
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document.write( "So \"cos%28B%29=adjacent%2F%28hypotenuse%29=2%2Fsqrt%2829%29=2sqrt%2829%29%2F29\"\r\n" );
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document.write( "-------------------------------------------------------\r\n" );
document.write( "
iii) evaluate sin^2(2A) + cos^2(2B).
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document.write( "We use the formulas and the two triangles above:\r\n" );
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document.write( "\"sin%282theta%29=2sin%28theta%29cos%28theta%29\" and\r\n" );
document.write( "\"cos%282theta%29=cos%5E2%28theta%29-sin%5E2%28theta%29\"\r\n" );
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document.write( "\"sin%282A%29=2sin%28A%29cos%28A%29=2%281%2Fsqrt%28145%29%29%2812%2Fsqrt%28145%29%29=24%2F145\" and\r\n" );
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document.write( "Now do yours step-by-step in every detail exactly like this one.\r\n" );
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document.write( "Edwin
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