# I need help on identities

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

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

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
Homework Helper
Gold Member
In what kind of problem might the expression tan x=2 occur?

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.

arildno
Homework Helper
Gold Member
Dearly Missed
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
Staff Emeritus
Gold Member
You don't need any identities to solve the system. Start by finding x...

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
Homework Helper
Yes, Cristo's answer was the simplest method.

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

robphy
Homework Helper
Gold Member
Ideally, the OP would have used my hint.

HallsofIvy