Use a double angle formula to find the exact value of the gi

Use a double angle formula to find the exact value of the given expression 1 - 2sin^2 22.5 degree 1 - 2 sin^2 22.5 degree = (Simplify your answer, including any radicals Use integers or fractions for any numbers in

Solution

1-2sin²22.5

cos 2theta=1-2sin²theta

Using the above formula we get

1-2sin²22.5=cos2(22.5)=cos 45=sqrt2/2