Hello Alyssa,

Given cos(x), we can first find sin(x). Using the well known identity **sin**^{2}**(x) + cos**^{2}**(x) = 1**, we have

sin^{2}(x) + (21/29)^{2} = 1

sin^{2}(x) + 441/841 = 1

sin^{2}(x) = 1 - 441/841

sin^{2}(x) = 400/841

sin(x) = ±20/29.

Note that the above gives two possible values for sin(x), but since 0° < x < 90° (x is in the first quadrant), we **choose the positive value.** That is,

**sin(x) = 20/29**

Now we see that

tan(x) = sin(x)/cos(x) = [20/29]/[21/29]

**tan(x) = 20/21**

Now use the double angle formula for tangent.

tan(2x) = 2tan(x)/[1 -tan^{2}(x)]

tan(2x) = 2(20/21)/[1 - (20/21)^{2}]

tan(2x) = (40/41)/[1 - 400/441] = (40/41)/[41/441] = (40/41)•(441/41)

**tan(2x) = 17640/1681**

Hope that helps! Let me know if you need any further explanation.

William