4tanx = 2(2tanx) / (2-2(sec^2x))

Question

Prove its right

Answer 1

First check that the supposed identity is correct by substituting a value for x. Let x=45°, so tan(x)=1. sec(x)=√2, sec²(x)=2.

LHS is 4tan(x)=4. RHS is 2(2)/(2-4)=4/-2=-2. So LHS≠RHS and the identity as false.

2-2sec²(x)=-2tan²(x), so 2(2tan(x))/(2-2sec²(x))=4tan(x)/(-2tan²(x))=-2cot(x).