tanx = 1/2
But we know that :
tanx = sinx/cosx = 1/2
==> 2sinx = cosx..........(1)
Also , we know that:
sin^2 x + cos^2 x = 1
==> cos x = sqrt(1-sin^2 x)..........(2)
Now substitute in (1)
==> 2sin x = sqrt(1-sin^2 x)
Square both sides:
==> 4sin^2 x = 1-sin^2 x
==> 5sin^2 x = 1
Divide by 5
==> sin^2 x = 1/5
==> sin x= 1/sqrt5= sqrt5/5
==> sin x = sqrt5/5
Now substitute in (1):
cosx = 2sinx
= 2(sqrt5/5)
= 2sqrt4/5
==> cos x = 2sqrt5/5