Question

Verify the basic identity. What is the domain of validity?

Answer 1

\[\cot \Theta = \cos \Theta \csc \Theta\]

Answer 2

@jim_thompson5910 could you help me please?

Answer 3

@Loser66 I couldn't see your equations

Answer 4

cot(x) = cos(x) * csc(x)

cot(x) = cos(x) * (1/sin(x))

cot(x) = cos(x)/sin(x)

cot(x) = cot(x)

Answer 5

cot(x) = cos(x)/sin(x)
csc(x) = 1/sin(x)

Answer 6

@jim_thompson5910 is cot(x) = cot(x) the answer?

Answer 7

well when you arrive at cot(x) = cot(x), the two sides are the same which means you have a confirmed identity

Answer 8

Oh okay I see! Thank you!

Answer 9

what exactly would be the domain of validity be?

Answer 10

what is the domain of cot(x)

Answer 11

I'm not sure, I don't really know how to find the domain of these

Answer 12

cot(x) = cos(x)/sin(x) right?

Answer 13

Yeah

Answer 14

so when is sin(x) equal to zero

Answer 15

When x = pi ?

Answer 16

where else

Answer 17

n?

Answer 18

what do you mean by n

Answer 19

Idk, would it be 1?

Answer 20

so you're saying x = 1 is also excluded?

Answer 21

No, I dont really know what else except for pi

Answer 22

how about x = 0?

Answer 23

I was going to say 0 but I wasn't sure

Answer 24

turns out the following values of x make sin(x) equal to zero

0, pi, 2pi, 3pi, 4pi, etc

so basically any multiple of pi makes sin(x) = 0

Answer 25

so that means you have to exclude these values of x to avoid dividing by zero

Answer 26

make sense?

Answer 27

yeah i get it

Answer 28

ok great