Question

How would you write the given expression as an algebraic expression of x?

sin(2arctan(x))

Answer 1

I'm getting (2x)/sqrt(x^2+1)

Answer 2

but the answer is (2x)/(x^2+1)

Answer 3

so you did u=arctan(x) => tan(u)=x
did you draw a right triangle for this?

Answer 4

also sin(2u)=2sin(u)cos(u)

Answer 5

yeah i drew a triangle

Answer 6

I think i know what you forget to do
did you multiply the bottoms?

Answer 7

as in like rationalize?

Answer 8

what did you get for sin(u) and cos(u)?

Answer 9

sin(u) = x/sqrt(x^2+1)
cos(u) = 1/sqrt(x^2+1)

Answer 10

ok great
\[2\sin(u)\cos(u)=2 \cdot \frac{x}{\sqrt{x^2+1}} \cdot \frac{1}{\sqrt{x^2+1}} =\frac{2 \cdot x \cdot 1}{\sqrt{x^2+1} \cdot \sqrt{x^2+1}}\]

Answer 11

remember when you multiply fractions
you multiply straight across on top
and straight across on bottom

Answer 12

ohh you have to use the double angle formula

Answer 13

yes because we have sin(2u)

Answer 14

i skipped that entire process and just did 2sin(u)

Answer 15

ok i got it thx

Answer 16

sin(2u) doesn't equal 2sin(u) for all u