## anonymous one year ago hey guys, need help is solving cos(2tan^-1x)

• This Question is Open
1. anonymous

what do you have to do with that function...

2. zepdrix

simplify probably :)

3. anonymous

yea fair call, probs a good idea to apply what arctanx means

4. zepdrix

$\large\rm \cos(2\color{orangered}{\arctan x})$ If $$\large\rm arctan x=\theta$$ then $$\large\rm \tan\theta=x$$ This arctangent is just some angle.$\large\rm \cos(2\color{orangered}{\arctan x})=\cos(2\color{orangered}{\theta})$So we need to apply our Double Angle Formula for Cosine. It shows up in three different forms, any of them will do.$\large\rm \cos(2\theta)=2\cos^2\theta-1$

5. zepdrix

We should draw a triangle to show what is going on with this tangent function.

6. zepdrix

$\large\rm \tan \theta=x\qquad\to\qquad \tan\theta=\frac{x}{1}=\frac{opposite}{adjacent}$

7. zepdrix

|dw:1444291200132:dw|

8. anonymous

|dw:1444291207356:dw|

9. zepdrix

Then use Pythagorean Theorem to find the missing hypotenuse.

10. anonymous

ye lel i'll delete mine

11. zepdrix

And use that information to finish it off

12. anonymous

probs a good idea to realise $\theta=\tan ^{-1}x$ and you therefore wants to find $\cos(2\theta)$

13. anonymous

then use trig identities

14. anonymous

all g?

15. anonymous

thanks guys.