I need help on identities

1. Mar 18, 2007

Mathslova

Can someone kindly help to find the exact values of cosx and sinx when tanx=2..

2. Mar 18, 2007

Moonbear

Staff Emeritus
Please show your own work on the problem so far so that the homework helpers know where to begin with helping you on this.

3. Mar 18, 2007

Mathslova

well i could have done it easily if it was in half angle form..i.e tan(1/2x)=2...i have some formulae to use but for that one i have no idea how to start

4. Mar 18, 2007

robphy

In what kind of problem might the expression tan x=2 occur?

5. Mar 18, 2007

cristo

Staff Emeritus
You don't really need a formula as such. Try drawing a diagram (i.e. a right angled triangle). You know the value of the tangent of one angle, so you should be able to write down the values of two of the sides. There's a theorem that you know to find the third side-- try using this.

6. Mar 18, 2007

arildno

Well, the simplest way is to utilize the identity:
$$\tan^{2}(x)+1=\frac{1}{\cos^{2}(x)}$$
If you are not familiar with that result, you should try to prove it first.

7. Mar 18, 2007

Hootenanny

Staff Emeritus
You don't need any identities to solve the system. Start by finding x...

8. Mar 18, 2007

Mathslova

Very much appreciated...I used SOHCAHTOA and got the answer I was looking for

9. Mar 18, 2007

HallsofIvy

Staff Emeritus
Yes, Cristo's answer was the simplest method.

(Darn, he got it in ahead of me!)

10. Mar 18, 2007

robphy

Ideally, the OP would have used my hint.

11. Mar 19, 2007

HallsofIvy

Staff Emeritus
I understand your point, but I can think of many problems involving tan x= 2 (or other values of tan x) that have nothing to do with right triangles.