document.write( "Question 1177724: Determine the constants a and b such that (-3 + 4(cos^2 x))/(1 - 2(sin x)) = a + b(sin x) for all values of x \n" ); document.write( "

Algebra.Com's Answer #806822 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) = .         ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained. And completed.\r
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\n" ); document.write( "\n" ); document.write( "This problem was posted to the forum a week or two ago, and I solved it under this link\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1177378.html\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1177378.html\r
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\n" ); document.write( "\n" ); document.write( "Here I simply pasted and copied that my solution for your convenience.\r
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\n" ); document.write( "\n" ); document.write( "E N J O Y (!)\r
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