find the exact value of the following
a) sin^2 45 + cos^2 45
b)2sin^2 45 + cos (2 * 45)
a) sin^2 45 + cos^2 45
Since sin^2(45) + cos^2(45) = 1 for any angle, the exact value is 1.
b) 2sin^2(45) + cos(2*45)
Using the double angle formula for cosine, cos(2*45) = cos(90) = 0.
Therefore, 2sin^2(45) + cos(2*45) = 2(1/2) + 0 = 1.