sin(75)=sin(30+45)=sin30.cos45+cos30.sin45=...
tan105=tan(60+45)=$\frac{tan60+tan45}{1-tan60.tan45}=...$
cos(-15)=cos(30-45)=cos30.cos45+sin30.sin45=...
$sin \frac{\pi}{12}=sin(\frac{\pi}{3}-\frac{\pi}{4})$
$cos \frac{22\pi}{3}=cos \frac{4\pi}{3}=cos(\frac{\pi}{3}+\pi)=....$
$sin \frac{23\pi}{4}=sin \frac{7\pi}{4}=sin( \frac{3\pi}{4}+\pi)=...$