document.write( "Question 1206962: 2tan(x)sin(x)+2sin(x)=tan(x)+1
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Algebra.Com's Answer #844702 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "    2tan(x)sin(x)+2sin(x)=tan(x)+1.\r\n" );
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document.write( "Collect everything in the left side\r\n" );
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document.write( "    2tan(x)sin(x) - tan(x) + 2sin(x) - 1 = 0.\r\n" );
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document.write( "Group the terms\r\n" );
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document.write( "    (2tan(x)sin(x) - tan(x)) + (2sin(x) - 1) = 0.\r\n" );
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document.write( "Factor\r\n" );
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document.write( "    tan(x)*(2sin(x)-1) + (2sin(x)-1) = 0,\r\n" );
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document.write( "    (tan(x)+1)*(2sin(x)-1) = 0.\r\n" );
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document.write( "Consider two cases.\r\n" );
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document.write( "    Case 1.  tan(x) +1 = 0  --->  tan(x) = -1  --->  x = 135°  or x = 315°.\r\n" );
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document.write( "    Case 2.  2sin(x)-1 = 0  --->  sin(x) = 1/2 --->  x =  30°  or x = 150°.\r\n" );
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document.write( "ANSWER.  The solutions are 30°, 135°, 150°, 315°.\r\n" );
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