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

Very much appreciated...I used SOHCAHTOA and got the answer I was looking forYou 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.
In what kind of problem might the expression tan x=2 occur?
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.Ideally, the OP would have used my hint.