document.write( "Question 1176721: If 0 < A < pi/2 and sinA + 1 = 2 sqrt(1-sin^2 A), determine the value of sinA. \n" ); document.write( "
Algebra.Com's Answer #804055 by MathLover1(20850)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "If \"0+%3C+A+%3C+pi%2F2+\"and \"sin%28A%29+%2B+1+=+2+sqrt%281-sin%5E2%28+A%29%29\", determine the value of \"sin%28A%29\".\r
\n" ); document.write( "\n" ); document.write( " \"sin%28A%29+%2B+1+=+2sqrt%281-sin%5E2%28A%29%29\".......square both sides\r
\n" ); document.write( "\n" ); document.write( " \"%28sin%28A%29+%2B+1%29%5E2+=+%282sqrt%281-sin%5E2%28A%29%29%29%5E2\"\r
\n" ); document.write( "\n" ); document.write( " \"%28sin%28A%29+%2B+1%29%5E2+=+4%281-sin%5E2%28A%29%29\"\r
\n" ); document.write( "\n" ); document.write( " \"sin%5E2%28A%29+%2B2sin%28A%29%2B+1=+4-4sin%5E2%28A%29\"\r
\n" ); document.write( "\n" ); document.write( "\"sin%5E2%28A%29+%2B4sin%5E2%28A%29%2B2sin%28A%29%2B+1-+4=0\"\r
\n" ); document.write( "\n" ); document.write( "\"5sin%5E2%28A%29%2B2sin%28A%29-+3=0\"......factor\r
\n" ); document.write( "\n" ); document.write( "\"5sin%5E2%28A%29-3sin%28A%29%2B5sin%28A%29-+3=0\"\r
\n" ); document.write( "\n" ); document.write( "\"%285sin%5E2%28A%29-3sin%28A%29%29%2B%285sin%28A%29-+3%29=0\"\r
\n" ); document.write( "\n" ); document.write( "\"sin%28A%29%285sin%5E2%28A%29-3%29%2B%285sin%28A%29-+3%29=0\"\r
\n" ); document.write( "\n" ); document.write( "\"%28sin%28A%29+%2B+1%29+%285sin%28A%29+-+3%29+=+0\"\r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "if \"sin%28A%29+%2B+1+=+0+\"=> \"sin%28A%29+=-1+\"
\n" ); document.write( "if \"5sin%28A%29+-+3+=+0\"=> \"sin%28A%29+=3%2F5\"\r
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\n" ); document.write( "\n" ); document.write( "\"A=sin%5E-1%28-1%29+=-pi%2F2\" ...........since given \"0+%3C+A+%3C+pi%2F2\", that is not solution\r
\n" ); document.write( "\n" ); document.write( "so, the value of \"sin%28A%29\" is \"3%2F5\"=> your solution\r
\n" ); document.write( "\n" ); document.write( "if you want angle in degrees, it is\r
\n" ); document.write( "\n" ); document.write( "\"A=sin%5E-1%283%2F5%29+=36.87\"°\r
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