document.write( "Question 1177378: Determine the constants a and b so that $\"+%28+-3+%2B++%28+4+cos%5E%28+2+%29+x+%29+%29+%2F+%28+1+-+2+sin+x+%29+=+a+%2B+b+sin+x+\"$ for all the values of x. Problem should be solved without a calculator. \n" ); document.write( "

Algebra.Com's Answer #806363 by ikleyn(52835) $\"\"$ $\"About$

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document.write( "The numerator is\r\n" );
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document.write( "    -3 + 4cos^2(x) = -3 + 4*(1-sin^2(x)) = 1 - 4sin^2(x) = (1-2sin(x))*(1+2sin(x)).\r\n" );
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document.write( "Now,   = \r\n" );
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document.write( "             (after canceling the factor (1-2sin(x)) in the numerator and denominator)\r\n" );
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document.write( "     = 1 + 2sin(x).\r\n" );
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document.write( "Therefore,  in this identity  a= 1,  b= 2.\r\n" );
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document.write( "Surely, the identity is valid only over the domain, which is  the entire number line excluding the roots of the denominator\r\n" );
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document.write( "    1 - 2sin(x) = 0,    i.e.  except   x= arcsin(1/2) = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained. And completed.\r
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