Question

Does sin(x)+sin(x)cot(x)=csc(x)

Answer 1

let's find out
first notice you can factor the left hand side

Answer 2

also is there suppose to be a square on cot?

Answer 3

nope, there is no square, my teacher just wanted us to prove (or disprove) if the equation was equivalent or not.

Answer 4

did you try pluggin in a value to see if both sides are the same or not

Answer 5

There was no value for x, I just put them there instead of the weird circle thingy that you use for cos sin and tan equations

Answer 6

I makes more sence to me then I put them back in later

Answer 7

no like finding a counterexample by choosing a value of x such that both sides are different

Answer 8

for example choose x =pi/6

Answer 9

are both side the same ?

Answer 10

\[\sin(\frac{\pi}{6})+\sin(\frac{\pi}{6}) \cot(\frac{\pi}{6})=? \\ \csc(\frac{\pi}{6})=?\]

Answer 11

Do I have to use values that I would find on the unit circle, or could I just plug in any number (ex 1 or 10, etc)

Answer 12

it doesn't matter what value of x you choose as long as it works to show the equation is false
the counterexample just means you are showing both sides aren't for all values of x and therefore the equation is not an identity
this is what you do if you believe the equation given is false

Answer 13

otherwise you might want to try to prove it if you don't have that belief

Answer 14

oh okay I just plugged in the equation with x=1 and the sides didn't match, so this proves that the two sides are NOT the same correct

Answer 15

that is right
if we tried to prove it
we get
sin(x)+sin(x)cot(x)
sin(x)[1+cot(x)]

and this doesn't seem to me giving us csc(x)
however if it was
sin(x)+sin(x)cot^2(x)
sin(x)[1+cot^2(x)]
sin(x)[csc^2(x)]
sin(x)*1/sin^2(x)
sin(x)/sin^2(x)
1/sin(x)
csc(x)
this would work

Answer 16

so again the equation you were given was not true since you were able to provide a counterexample... that example you chose was x=1

Answer 17

awesome!!! Thanks a whole bunch!!

Answer 18

np