csc x(2sinx- sqrt 2) =0
Trigonometric function or not?

Question

csc x(2sinx- sqrt 2) =0
Trigonometric function or not?

zepdrix · Answer

What is it that you're asking?
$$\Large\rm \csc x\left(2\sin x-\sqrt2\right)=0$$Solve for x?

anonymous · Answer

i need to figure out if it's a trigonometric identity or not

anonymous · Answer

I didn't mean function, sorry :x

zepdrix · Answer

Are you sure you read the directions correctly? 0_o
This sure looks like a "solve for x" problem.
Hmm

anonymous · Answer

yeah, it says "decide whether the equation is a trigonometric identity"

zepdrix · Answer

$\Large\rm \csc x$ is equivalent to $\Large\rm \dfrac{1}{\sin x}$. So that gives us$$\Large\rm \frac{1}{\sin x}\left(2\sin x-\sqrt2\right)=0$$Distributing that to the bracketed stuff gives us,$$\Large\rm 2-\frac{\sqrt2}{\sin x}=0$$When we're trying to verify whether or not something is an identity, we only alter one side and try to make it match the other side.

zepdrix · Answer

So in this case, yes there are specific x values which will give us 0 on the left side, making this true,
but it is certainly not an identity. >.<

zepdrix · Answer

Weird stuff :U

anonymous · Answer

yeah, it is. Thank you a lot, though. That makes sense C: