Question

If Tanα=√2-1 then α=?

Answer 1

tanα=sinα/cosα
[(tanα)^2][(cosα)^2] = (sinα)^2

We know that (cosα)^2 =1 - (sinα)^2
Therefore,
[(tanα)^2][1-(sinα)^2] = (sinα)^2
⇒ (tanα)^2 - [(tanα)^2][(sinα)^2] = (sinα)^2
⇒ (tanα)^2 = [(sinα)^2][1 + (tanα)^2]
⇒ [(tanα)^2]/[1 + (tanα)^2] = (sinα)^2

Since we are already given the value of tanα,we can calculate the value of sinα

sinα = √{[(tanα)^2]/[1 + (tanα)^2]}

Please note that you will get both a negative and positive value for sinα.

Using these values, we can also calculate cosα
cosα = sinα/tanα.

Alternatively, 
If the value of tanα is given in fractions, ( or can be easily converted into them), we can calculate values of sinα and cosα with another method.

let tanα=a/b
sinα = (a)/√(a^2 + b^2)
cosα = (b)/(a^2 + b^2)