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How do i find

cos(2arctan(7/24))

Thanks.

1 answer

A right triangle with sides of 7 and 24 has a hypotenuse of 25. The cosine of arctan 7/24 is 24/25 and the sine is 7/25.
Now use the formula
cos2A = cos^2A - sin^A
to arrive at
cos(2arctan(7/24))
= (24/25)^2 - (7/25)^2 = 527/625

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