$H=\cos\alpha+\sin\alpha.\dfrac{\cos\alpha}{\sin\alpha}+\dfrac{1-2\cos^2\alpha}{\sin\alpha-\cos\alpha}$
$=\cos\alpha+\cos\alpha+\dfrac{1-\cos^2\alpha-\cos^2\alpha}{\sin\alpha-\cos\alpha}$
$=2\cos\alpha+\dfrac{\sin^2\alpha-\cos^2\alpha}{\sin\alpha-\cos\alpha}$
$=2\cos\alpha+\dfrac{(\sin\alpha-\cos\alpha)(\sin\alpha+\cos\alpha)}{\sin\alpha-\cos\alpha)}$
$=2\cos\alpha+\sin\alpha+\cos\alpha$
$=\sin\alpha+3\cos\alpha$
