Simplfiying Trig Functions

Question

Write the given expression as an algebraic expression in x.

cos(2 cos⁻¹ x)

Answer 1

cos( 2 cos⁻¹ x ) = 2 cos( cos⁻¹ x )² - 1 = 2x² - 1

∴ cos( 2 cos⁻¹ x ) = 2x² - 1

I hope this helps to take the trigonometric expression to a strictly algebraic expression in x. Message me in the comments if you have any questions, comments, or concerns.