Find the exact value of the expression sintan1 2 2 squareroo

Find the exact value of the expression: sin(tan^-1 2) 2 squareroot 5 2 squareroot 5/5 5 squareroot 2 5 squareroot 2/2

let tan^-1 2 = x

=> tanx = 2

hence sin x = 2/ sqrt (2^2 +1^2) = 2/ sqrt (4+1) =2/ sqrt (5)

We have assumed tan^-1 2 = x , hence we have

sin (tan^-1 x) = sinx and we got the value for sinx = 2/ sqrt (5)

Therefore sin (tan^-1 x) = 2/ sqrt (5)

Now multiply numerator and denominator with sqrt 5 we get

sin (tan^-1 x) = 2/ sqrt (5) = (2* sqrt5)/ (sqrt5*sqrt5) = (2sqrt5)/ 5

b is the correct option.