If sin (x) = 1/3 and sec (y) = 13/12, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (Enter an exact answer.) cos (2y)

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Mathematics

Thomas Bird

11 September, 06:33

If sin (x) = 1/3 and sec (y) = 13/12, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (Enter an exact answer.) cos (2y)

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Sage Short · Answer 1

Since sec (y) = 1/cos (y), cos (y) = 1 / (13/12) = 12/13. In addition, since

cos (2y) = 2cos^2 (y) + 1, we can plug cos (y) = 12/13 in to get 2 (12/13) ^2+1

=2 (12^2/13^2) + 1=2 (144/169) + 1=288/169+1=288/169+169/169=457/169