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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

Verified Answer :

arthurpdc

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

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

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