Question

Verify the Pythagorean Identity.

Answer 1

Are you familiar with the property sin²(x)+cos²(x)=1 ?

Answer 2

not really, I don't really understand this stuff but if you would like to explain it and help me work it out I would be very grateful

Answer 3

Sorry for the wait, I was working on another problem

Answer 4

It's OK. It's relevant to the Pythagorean Identity and the unit circle:
A number x in the unit circle coordinates' are (cos(x),sin(x)).
From the drawing you can see that using the Pythagorean Identity, we get sin²(x)+cos²(x)=1

Answer 5

From that you just divide by sin²(x) to get the requested Pythagorean Identity.

Answer 6

So it's like the Pythagorean theorem but different?

Answer 7

I still don't understand how I would word that? Like
sin²(x)+cos²(x)=1/sin^2(x)

Answer 8

It's exactly like Pythagorean theorem, applied to the unit circle.

Answer 9

No you have to divide both the RHS and the LHS !
1/sin²(x) * (sin²(x)+cos²(x)) = 1/sin²(x) * 1
=> 1 + cot²(x) = csc²(x)

Answer 10

Okay I think I understand now