I need help on identities

[Mathslova]

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

 

[Moonbear]

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

 

[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

 

[robphy]

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

 

[cristo]

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.

 

[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.

 

[Hootenanny]

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

 

[Mathslova]

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.

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

 

[HallsofIvy]

Yes, Cristo's answer was the simplest method.

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

 

[robphy]

Ideally, the OP would have used my hint.

 

[HallsofIvy]

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

Ideally, the OP would have used my hint.

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.