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

Algebra ->  Trigonometry-basics -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!


%28sin%2841%29%2Bcos%2841%29%29%5E2+=+2sin%5E2%28x%29

Expand on the left:

sin%5E2%2841%29%2B2sin%2841%29cos%2841%29%2Bcos%5E2%2841%29+=+2sin%5E2%28x%29

Use sin^2+cos^2=1:

1%2B2sin%2841%29cos%2841%29+=+2sin%5E2%28x%29

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

1%2Bsin%2882%29+=+2sin%5E2%28x%29

Solve for sin(x):

sin%28x%29+=+sqrt%28%281%2Bsin%2882%29%29%2F2%29

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

sin%28x%29+=+sqrt%28%281%2Bcos%288%29%29%2F2%29

Use half angle formula for cosine:

sin%28x%29+=+cos%284%29

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

sin%28x%29+=+sin%2886%29

ANSWER: 86 degrees