find cos( 2x) =?

Question

If  (in Quadrant-I),

Answer 1

If sec(x) = 43 then (because sec(x) = 1/cos(x)), cos(x) = 1/43.

An identity for cos(2x) is:

cos(2x) = 2cos²(x) – 1

So we can say cos(2x) = 2(1/43)² - 1 = 2(1/1849) - 1 = 2/1849 - 1849/1849 = -1847/1849