91Ó°ÊÓ

$$ \cos 255^{\circ}+\sin 165^{\circ}=0 $$

$$ \sin 50^{\circ}-\sin 70^{\circ}+\sin 10^{\circ}=0 $$

$$ (\sin 3 A+\sin A) \sin A+(\cos 3 A-\cos A) \cos A=0 $$

$$ \tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}=4 $$

$$ \sin a \sin \left(60^{\circ}-a\right) \sin \left(60^{\circ}+a\right)=\frac{1}{4} \sin 3 a $$

$$ \text { If } \frac{\cos \alpha}{\cos \beta}=n, \frac{\sin \alpha}{\sin \beta}=m, \text { show that }\left(m^{2}-n^{2}\right) \sin ^{2} \beta=1-n^{2} \text { . } $$