Question

tan(2 cos^(−1) x)

Write the expression algebraically in x

Answer 1

Hmm, might be able to simplify this by drawing the right triangle.

Answer 2

\(cos^{-1}x means the angle, say Θ, that has a cosine of x/1.

Answer 3

Change tan into sin/cos and you can convert using double angle formula.

Answer 4

You're basically looking for tan(2Θ).
The double angle identity is

\[\large tan(2Θ) = \frac{2tan(Θ)}{1-tan^2(Θ)}\]

Answer 5

I don't know if this is right, but I half-awake scratched this on some paper:

\(-2x\sqrt{1-x^2}\)

See if you can get that.

Good luck and good night.