Trig identities, prove (cot(x)-tan(x)=2tan(2x))

[noahsdev]

Homework Statement

Prove cot(x) - tan(x) = 2tan(2x)

Homework Equations

Trig identities
http://en.wikipedia.org/wiki/List_of_trigonometric_identities

The Attempt at a Solution

I have worked it down and don't think they are equal. I think it's supposed to be 2cot(2x) not 2tan(2x), that is what I found. Am I correct or what have I done wrong?
Thanks

 

[CAF123]

Yes, I get the same result as you, although your calculation was a lot more complicated. If you let x=π/4, the LHS is zero while the RHS is undefined. So it cannot be 2tan(2x) for the equation to be an identity.

 

[noahsdev]

Thanks for the fast reply, my teacher wanted full working with identities so that's why it's in long form. I am not sure if it is a mistake or if it is a trick question, thanks.

 

[CAF123]

Thanks for the fast reply, my teacher wanted full working with identities so that's why it's in long form. I am not sure if it is a mistake or if it is a trick question, thanks.

Most likely a mistake unless the question wanted you to find what particular subset of x satisfies the equation. But if it says 'Prove..' then that is not the case.