Prove the identity (4cos(2x))/(1+cos(2x)) = 4-2sec^2(x)

Write down the formulas involving cos2x and select the one which involves only cosine, this is because cosine (or derivations of it) is the only trigonometric function in this question. Substitute the chosen identity which is cos(2x) = 2cos^2(x)-1 into the left handside (LHS) of the equation which should give you: (8cos^2(x) - 4)/(2cos^2(x))   This can be cancelled down to 4-2/cos^2(x) Manipulate the right handside (RHS) of the equation by using the identity: sec(x) = 1/cos(x). This should give the RHS to be 4-2/cos^2(x) which = LHS. Make it obvious to the examiner that the sides of the are equal by equating them at the end so you don't lose marks!