Question

Evaluate: cos(2arctan(1/3))

I used the double angle identity cos(2x) = cos^2x-sin^2x
cos(2x)= (3/sqrt(10))^2- (1/sqrt(10))^2 = 2/25
2/25 was my answer to this problem but the correct answer was 4/5
How is the correct answer 4/5?? I thought I did everything right

Answer 1

Possibly you are making the account considering that the denominator of fractions that are squared are 10. Look:


`\cos(2x)= \left((3)/(√(10))\right)^2- \left((1)/(√(10))\right)^2 = (9)/(10)-(1)/(10)=(8)/(10)=\boxed{(4)/(5)}`