Question

vertify the identities: cscx - sinx =cosx cotx

Answer 1

cscx - sinx = cosx*cotx
1/sinx - sinx = cosx*cosx/sinx

multiply both sides by sinx

1 - sin^2(x) = cos^2(x) --> sin^2(x) + cos^2(x) = 1

Yep, this is true. That is a very popular identity.

Answer 2

I was taught that you could only touch one side of the equation. So how I would verify it is by changing the left side of the equation. I would multiply sinx by 1, or sinx/sinx to get 1/sinx- sin^2/sinx. I would add them because they have common denominators and convert 1-sin^2x to cos^2x, so cos^2x/sinx. cosx/sinx=cotx so cosx cotx