document.write( "Question 1134822: If tan(A+B) = 1/7 and tanA = 3, find without using tables, the value of tanB. \n" ); document.write( "
Algebra.Com's Answer #752346 by ikleyn(52784)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The way on how the other tutor resolved this problem/question,  is formally correct, \r
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\n" ); document.write( "\n" ); document.write( "            but this problem can be solved in  MUCH  EASIER  way.\r
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\n" ); document.write( "\n" ); document.write( "            What is even more important, this problem  IS  DESIGNED  and  IS  INTENDED  to be solved by the other,  more simple way.\r
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\n" ); document.write( "\n" ); document.write( "            See my solution below.\r
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document.write( "The identity  (A + B) - A = B  directly instructs and prescribes you to use the formula of difference for tangent function,\r\n" );
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document.write( "which originally has the form\r\n" );
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document.write( "    tan(x - y) = \"%28tan%28x%29-tan%28y%29%29%2F%281%2Btan%28x%29%2Atan%28y%29%29\"\r\n" );
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document.write( "Using this formula, you should take x = A+B, y = A  to get\r\n" );
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document.write( "    tan(B) = tan((A+B) -A) = \"%28tan%28A%2BB%29+-+tan%28A%29%29%2F%281+%2B+tan%28A%2BB%29%2Atan%28B%29%29\" = \r\n" );
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document.write( "        now substitute the given values  tan(A+B) = \"1%2F7\"  and  tab(B) = 3  to get\r\n" );
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document.write( "  = \"%28%281%2F7+-+3%29%29%2F%28%281+%2B+%281%2F7%29%2A3%29%29\" = \"%28%281-3%2A7%29%2F7%29%2F%28%287%2B3%29%2F7%29\" = \"%28%28-20%2F7%29%29%2F%28%2810%2F7%29%29\" = \"-20%2F10\" = -2.    ANSWER\r\n" );
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document.write( "In this way, the problem is just SOLVED.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice, that this solution  DOES  NOT  REQUIRE  reducing the problem to some equation and solving it.\r
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\n" ); document.write( "\n" ); document.write( "It only requires to make one line simple calculations based on well known Trigonometry formula.\r
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\n" ); document.write( "\n" ); document.write( "If my solution seems complicated to you from the first glance  (although it is as simple as possible),\r
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\n" ); document.write( "\n" ); document.write( "I will repeat it one more time,  by omitting accompanying explanations - they are needed only for the first time:\r
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document.write( "    tan(B) = tan((A+B) -A) = \"%28tan%28A%2BB%29+-+tan%28A%29%29%2F%281+%2B+tan%28A%2BB%29%2Atan%28B%29%29\" = \"%28%281%2F7+-+3%29%29%2F%28%281+%2B+%281%2F7%29%2A3%29%29\" = \"%28%281-3%2A7%29%2F7%29%2F%28%287%2B3%29%2F7%29\" = \"%28%28-20%2F7%29%29%2F%28%2810%2F7%29%29\" = \"-20%2F10\" = -2.  \r\n" );
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\n" ); document.write( "\n" ); document.write( "This one line version is how the solution should be and must be presented when you know the way on how to solve it . . . \r
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\n" ); document.write( "\n" ); document.write( "Once again: my post is the way on how this problem expected and intended to be solved.\r
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\n" ); document.write( "\n" ); document.write( "The other's tutor solution is a wrong approach to the problem.\r
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