Question

cos^2 22.5 - sin^2 22.5

Answer 1

Cos^2x-sin^2x=cos2x, tak chto cos^2(22.5)-sin^2(22.5)=cos45=sqrt2/2

Answer 2

cos^2(22.5) - sin^2(22.5)

Using the double angle formula for cosine and sine, we can express cos^2(22.5) and sin^2(22.5) in terms of cos(45) and sin(45):

cos^2(22.5) = (1 + cos(45))/2 sin^2(22.5) = (1 - cos(45))/2

Substituting these expressions into the original equation, we get:

(1 + cos(45))/2 - (1 - cos(45))/2 = (1 + cos(45) - 1 + cos(45))/2 = 2cos(45)/2 = cos(45) = 1/√2

So, cos^2(22.5) - sin^2(22.5) = 1/√2.