Buktikanlah identitas trigonometri berikut ini: (tan α + sin α) (1-cos α)=sin² α tan α

[tex]$\begin{align}(\tan a+\sin a)(1-\cos a)&=\tan a-\tan a\cdot\cos a+\sin a-\sin a\cos a\\&=\tan a-\frac{\sin a}{\cos a}\cdot\cos a+\sin a-\sin a\cos a\\&=\tan a-\sin a+\sin a-\sin a\cos a\\&=\tan a-\sin a\cos a\\&=\frac{\sin a}{\cos a}-\frac{\sin a\cos^2a}{\cos a}\\&=\frac{\sin a(1-\cos^2a)}{\cos a}\\&=\frac{\sin a\times\sin^2a}{\cos a}\\&=\sin^2a\times\frac{\sin a}{\cos a}\\&=\boxed{\sin^2a\cdot\tan a}\ \bold{(terbukti)}\end[/tex]