document.write( "Question 1153168: If (cos41 degrees + sin 41 degrees)^2=2sin^2(A), where A is between 0 and 90 degrees, compute the degree measure of angle A \n" ); document.write( "

Algebra.Com's Answer #775336 by greenestamps(13206) $\"\"$ $\"About$

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\n" ); document.write( " $\"%28sin%2841%29%2Bcos%2841%29%29%5E2+=+2sin%5E2%28x%29\"$

\n" ); document.write( "Expand on the left:

\n" ); document.write( " $\"sin%5E2%2841%29%2B2sin%2841%29cos%2841%29%2Bcos%5E2%2841%29+=+2sin%5E2%28x%29\"$

\n" ); document.write( "Use sin^2+cos^2=1:

\n" ); document.write( " $\"1%2B2sin%2841%29cos%2841%29+=+2sin%5E2%28x%29\"$

\n" ); document.write( "Use sin(2x) = 2sin(x)cos(x):

\n" ); document.write( " $\"1%2Bsin%2882%29+=+2sin%5E2%28x%29\"$

\n" ); document.write( "Solve for sin(x):

\n" ); document.write( " $\"sin%28x%29+=+sqrt%28%281%2Bsin%2882%29%29%2F2%29\"$

\n" ); document.write( "Use sin(x) = cos(90-x) for acute angles:

\n" ); document.write( " $\"sin%28x%29+=+sqrt%28%281%2Bcos%288%29%29%2F2%29\"$

\n" ); document.write( "Use half angle formula for cosine:

\n" ); document.write( " $\"sin%28x%29+=+cos%284%29\"$

\n" ); document.write( "Use sin(x) = cos(90-x) for acute angles:

\n" ); document.write( " $\"sin%28x%29+=+sin%2886%29\"$

\n" ); document.write( "ANSWER: 86 degrees

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