how can you simplify (sin2x)/x ?

Question

there is a way to simplify it, but i keep coming to a dead end.

i haven't had this type of question in a while, so im pretty rusty, thnx for helping me!

Answer 1

well here i can give 2 formulas of sin2x
1 - sin2x = 2sinx.cosx
2 - sin2x = (2tanx) / ( 1+tan^2x)

But i think Equations must contain a single = sign.
i mean something like this (sin2x)/x = 0 , so we can work better .
any way good luck.

Answer 2

There is no simplification of this function. It is possible to find the limit as x->0, but that is not the same thing by a long shot. The limit is 2.

Answer 3

sin 2x = 2sinx cosx

What exactly do you want to do further??

In terms of pure x,

sinx = x - x^3/3! + x^5/5! - x^7/7! +....

so, for sin 2x, just replace x in the above equation by 2x

Divide it then by x and you get

sin2x /x = 2 - 8x^2/6 + 1/x [(2x)^5/5! - (2x)^7/7! + ...]

Answer 4

shouldn't the simplification just be sin2? you divide out the x, right?

Wow I guess I'm no math genius. I should have known better then to f*** around with a question with trig stuff.

Answer 5

Well sin(2x) is the same as 2sin(x)cos(x) but that doesn't really help with simplifying.

Answer 6

The espression can be made more complicated, but it is already in its simplest form.