Question

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

Answer 1

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

Answer 2

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

Answer 3

I didn't mean function, sorry :x

Answer 4

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

Answer 5

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

Answer 6

\(\Large\rm \csc x\) 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.

Answer 7

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. >.<

Answer 8

Weird stuff :U

Answer 9

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