Cos X + 1 / cos X=40, find the value of cos square X + 1 / cos square X

This is pseudo-trig. It has a trig function but it's irrelevant.

Let y = cos X

y + 1/y = 40

Squaring,

y² + 2 (y) (1/y) + 1/y² = 1600

y² + 2 + 1/y² = 1600

y² + 1/y² = 1598

cos² X + 1/cos²X = 1598

Answer: 1598