document.write( "Question 926811: If sinA+cosA=sqrt(2) then, A=45, how? \n" ); document.write( "
Algebra.Com's Answer #562475 by rothauserc(4718)\"\" \"About 
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we are given
\n" ); document.write( "sinA + cosA = sqrt(2)
\n" ); document.write( "square both sides of =
\n" ); document.write( "sin^2(A) + 2sinAcosA + cos^2(A) = 2
\n" ); document.write( "use identity sin^2(A)+cos^2(A) = 1
\n" ); document.write( "2sinAcosA +1 = 2
\n" ); document.write( "subtract 1 from both sides of =
\n" ); document.write( "2sinAcosA = 1
\n" ); document.write( "divide both sides of = by 2
\n" ); document.write( "sinAcosA = 1/2
\n" ); document.write( "now substitute 45 degrees for A
\n" ); document.write( "sin(45)*cos(45) = 1/2
\n" ); document.write( "0.707106781 * 0.707106781 = 1/2
\n" ); document.write( "0.5 = 0.5
\n" ); document.write( "answer checks, A = 45 degrees
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