document.write( "Question 1108772: If A and B are acute angles such that sin(A) = 3/5 and cos(B) = 5/13, find tan(A+B) without evaluating A or B \n" ); document.write( "
Algebra.Com's Answer #723782 by ikleyn(52782)\"\" \"About 
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document.write( "1.  If  sin(A) = \"3%2F5\",  then  cos(A) = \"sqrt%281-sin%5E2%28A%29%29\" = \"sqrt%281-%283%2F5%29%5E2%29\" = \"sqrt%281-9%2F25%29\" = \"sqrt%28%2825-9%29%2F25%29\" = \"sqrt%2816%2F25%29\" = \"4%2F5\",  and, hence,  tan(A) = \"sin%28A%29%2Fcos%28A%29\" = \"%28%283%2F5%29%29%2F%28%284%2F5%29%29\" = \"3%2F4\".\r\n" );
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document.write( "2.  If  cos(B) = \"5%2F13\",  then  sin(B) = \"sqrt%281-cos%5E2%28B%29%29\" = \"sqrt%281-%285%2F13%29%5E2%29\" = \"sqrt%281-25%2F169%29\" = \"sqrt%28%28169-25%29%2F169%29\" = \"sqrt%28144%2F169%29\" = \"12%2F13\",  and, hence,  tan(B) = \"sin%28B%29%2Fcos%28B%29\" = \"%28%2812%2F13%29%29%2F%28%285%2F13%29%29\" = \"12%2F5\".\r\n" );
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document.write( "3.  Now  tan(A+B) = \"%28tan%28A%29+%2B+tan%28B%29%29%2F%281+-+tan%28A%29%2Atan%28B%29%29\" = \"%283%2F4%2B12%2F5%29%2F%281-%283%2F4%29%2A%2812%2F5%29%29\" = \"%28%2815%2B48%29%2F20%29%2F%28%281-36%2F20%29%29\" = \"%28%2863%2F20%29%29%2F%28%281-36%2F20%29%29\" = \"%28%2863%2F20%29%29%2F%28%28-16%2F20%29%29\" = \"-63%2F16\".\r\n" );
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