NEED ASAP! use a right triangle and a double angle formula to write tan(2 cos^-1 x) as an algebraic expression. simplify completely.

Question

tan ( 2 cos^-1 x)

Answer 1

let θ = cos^-1(x)

cos(θ) = x/1

sin(θ) = √(1-x²)/1

tan(θ) = √(1-x²)/x

tan(2θ) = 2tan(θ)/(1-tan²(θ)) = 2(√(1-x²)/x)/(1-(√(1-x²)/x)²) = 2(√(1-x²)/x)/(1-(1-x²)/x²)

= 2x√(1-x²) / (2x²-1)