Which of the following expressions is equivalent to (cos(3x))/sin(x)cos(x))?

Question

csc(x) cos(2x) - sec(x) sin(2x)
sec(x) cos(2x) - csc(x) sin(2x)
sec(x) cos(x) - csc(x) sin(x)
csc(x) cos(x) - sec(x) sin(x)

This is my last question and I've tried solving it repeatedly but now I think I'm stuck... can someone please help?

Answer 1

Hmmm. cos(3x) = cos(2x) cosx - sin(2x) sinx
divide that by sinx cosx and you have

cos(2x)/sinx - sin(2x)/cosx
= cos(2x) cscx - sin(2x) secx
Looks like (A) to me

Answer 2

Yes, it was A:) Thank you, Steve!