Prove that 2 cot (2x) + tan(x) == cot (x)

(1) Aim to rearrange the right hand side (rhs) to make it look like the left hand side.LHS = 2 cot (2x) + tan (x)(2) Notice that the rhs is only in terms of x, whereas the right has a function involving 2x. Therefore use trig identities to make the RHS in terms of x onlycot (2x) = 1 / tan (2x) = [1 - tan ² (x)]/[(2 tan (x))]ThereforeLHS = [1 - tan ² (x)]/[ tan (x)] + tan (x) = 1 / tan(x) = cot (x) = RHS, as given.