Question

Using a graphing calculator to make a conjecture as to wether each equation is an identity.sin 2x = 2 sin x

Answer 1

Let's make a graph of each side of our equation:

From the given graph, we can note that both graph are intersect each other when

x is multiple of Pi, that is,

`x=\ldots-n\pi,\ldots,-3\pi,-2\pi,0,\pi,2\pi,\ldots..,n\pi`

which can be written as

`x=n*\pi\text{ }`

with n denoting an integer number.

Therefore, the equation is an identity when

`x=n*\pi\text{ with n}\in\text{ Integer}`