SOLUTION: 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

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
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Expand on the left:

Use sin^2+cos^2=1:

Use sin(2x) = 2sin(x)cos(x):

Solve for sin(x):

Use sin(x) = cos(90-x) for acute angles:

Use half angle formula for cosine:

Use sin(x) = cos(90-x) for acute angles:

ANSWER: 86 degrees

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