Simplifying Trig Functions

Question

Write the given expression as an algebraic expression in x.

cos(2 cos⁻¹ x)

Answer 1

Hi,

cos(2 cos⁻¹ x) =?

you know : cos⁻¹ x = ∝ ------> cos ∝ = x then replace to the question:

cos(2 cos⁻¹ x) = cos(2 ∝) = 2 cos² ∝ - 1 = 2 x² -1 Base of double angle formula

I hope it is useful,

Minoo

Answer 2

θ = cos^-1 x

Use the double angle formula.