document.write( "Question 1089267: if tan a and tan b are the roots of equation 4x^2-7x+1=0 then evaluate 4sin^2(a+b)-7sin(a+b)cos(A+B)+cos^2(A+B) \n" ); document.write( "

Algebra.Com's Answer #703616 by ikleyn(52909) $\"\"$ $\"About$

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\n" ); document.write( "if tan a and tan b are the roots of equation 4x^2-7x+1=0 then evaluate 4sin^2(a+b)-7sin(a+b)cos(A+B)+cos^2(A+B)
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document.write( "if tan(a) and tan(b) are the roots of equation 4x^2-7x+1=0 then\r\n" );
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document.write( "    tan(a) + tan(b) =   and  tan(a)*tan(b) = ,    (1)\r\n" );
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document.write( "according to Vieta's formulas/theorem.\r\n" );
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document.write( "It implies  tan(a+b) =  =  =  =   and then   =  =  =  =  = .       (2)\r\n" );
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document.write( "Then  \r\n" );
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document.write( "   =  =  =  = \r\n" );
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document.write( "=  =  = .\r\n" );
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document.write( "Substitute here   =   from (2),  and you will get\r\n" );
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document.write( " = . . . =  = 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The value under the question is 1.\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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