Question

How do you prove `cot2x = (1+cos4x) / (sin4x)`?

Answer 1

We will use the following identities:

• `sin(2theta) = 2sin(theta)cos(theta)`

• `cos(2theta) = 2cos^2(theta) - 1`

Now, starting from the right hand side:

`(1+cos(4x))/sin(4x) = (1+(2cos^2(2x)-1))/(2sin(2x)cos(2x))`

`= (2cos^2(2x))/(2sin(2x)cos(2x))`

`= cos(2x)/sin(2x)`

`= cot(2x)`