Verify trigonometry equation $\tan A - \csc A \sec A (1-2\cos^2 A)= \cot A$ How would I verify the following trigonometry identity?
$$\tan A - \csc A \sec A (1-2\cos^2 A)= \cot A$$
My work so far is 
$$\frac{\sin A}{\cos A}-\frac{1}{\sin A}\frac{1}{\cos A}(1- \cos^2 A- \cos^2 A)$$

$$\frac{\sin A}{\cos A}-\frac{1-2\cos^2 A}{\sin A \cos A}=\cot A$$
By the pythagorean identity, $1-2\cos^2 A=\sin^2 A-\cos^2 A$.
$$\frac{\sin A}{\cos A}-\frac{\sin^2 A -\cos^2 A}{\sin A \cos A}=\cot A$$
If I told you to split up the fraction, could you get it from there?
