## lgg23 4 years ago Calculus: tan (2 arc cos (x/3)) = ?

1. anonymous

What are you supposed to do? Integrate, derive, solve for x...?

2. lgg23

it says to simplify the expression

3. asnaseer

Since we know arccos(x/3) gives us an angle $$\alpha$$ whose cosine is x/3, we can draw the following triangle and use Pytharogus to calculate the length of the third side: |dw:1328486495106:dw| From this we get:$\tan(\alpha)=\frac{\sqrt{9-x^2}}{x}\tag{a}$Now just use the formula for $$\tan(2\alpha)$$ to get:$\tan(2\alpha)=\frac{2\tan(\alpha)}{1-\tan^2(\alpha)}\tag{b}$Substitute equation (a) into equation (b) and simplify.

4. lgg23

Thank you.

5. asnaseer

yw