find cos ( 2 x ) =

Question

If  (in Quadrant-I),

Answer 1

Since tan(x) = opposite/adjacent and tan(x) = 78 = 78/1 then the opposite side is 78 and the adjacent side is 1 like this (since we are talking Q1):

Using the Pythagorean Theorem, the hypotenuse is √(1² + 78²) = √6085

So cos(x) = adjacent/hypotenuse = 1/√6085

Using the identity cos(2x) = 2cos²(x) – 1 we can say cos(2x) = 2(1/√6085)² - 1 = 2/6085 - 6085/6085 = -6083/6085