We will start off working on the right hand side. <span>cot x - tan x </span> <span>= [cos x / sin x] - [sin x / cos x] </span> <span>= [(cos x)^ 2 - (sin x)^2] / [sin x cos x] </span>
<span>This is where it gets a bit tougher if you do not have your formula list with you. </span> <span>(cos x)^ 2 - (sin x)^2 = cos(2x) </span> <span>sin 2x = 2 sin x cos x </span>
<span>Note that by arranging the second formula, we will have sin x cos x = (1/2) sin 2x </span>
<span>Hence, we will get: </span> <span>[(cos x)^ 2 - (sin x)^2] / [sin x cos x] </span> <span>= [cos 2x] / (1/2)[sin 2x] </span> <span>= 2[cos 2x] / [sin 2x] </span> <span>= 2cot 2x </span>
