document.write( "Question 1176724: If x > 0, $\"+%28+arcsin+%28+x%2F2+%29+%2B+arccos+%28+x%2F2+%29+%29+%2F+arctan+%28+x+%29+=+3%2F2+\"$ , solve for x. \n" ); document.write( "

Algebra.Com's Answer #804174 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "if x > 0, solve for x $\"%28arcsin%28x%2F2%29+%2B+arccos%28x%2F2%29%29%2Farctan%28x%29\"$ = $\"3%2F2\"$ .\r
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document.write( "Let a = ,  b = .\r\n" );
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document.write( "It means that  \r\n" );
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document.write( "    sin(a) = ;  cos(b) =   and  \"a\"  and  \"b\"  are the angles in QI  (acute angles).\r\n" );
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document.write( "Since  sin(a) = cos(b),  it means that  a + b = .\r\n" );
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document.write( "In other words, the numerator in our fraction, which is   + , is equal to  .\r\n" );
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document.write( "Thus our original equation is   = .\r\n" );
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document.write( "It implies  arctan(x) =  = .\r\n" );
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document.write( "Since  arctan(x) = ,  it implies  x =  = .\r\n" );
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document.write( "ANSWER.  x = .\r\n" );
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