can someone please help with this trig question

[M-D]

i need to solve the following question without a calculator:

If tan(x)=2 and x is an element of [0,pi/2], use trigonometric identities to find the exact value of sin(2x)?

this is what i have done:

sin(2x)=2sin(x)cos(x)

tan(x)=sin(x)/cos(x)=2

therefore, sin(x)=2cos(x)

and sin(2x)=4[cos(x)]^2

i don't know what to do next.

i appreciate your help

[mark_alec]

If tan(x) = 2, you can draw a right angled triangle with the lengths: opposite=2, adjacent=1, hypotenuse=sqrt(5).

Then using the double angle formula, you know that sin(2x) = 2sin(x)cos(x), and reading from the triangle, it can be seen that sin(x)=2/sqrt(5) and cos(x)=1/sqrt(5).

[M-D]

thanks a lot. i got the right answer. i appreciate your help