jumlah sin 75°- sin 165°

sin (90-15)° - sin (180-15)°
= cos 15° - sin 15°
= cos (45-30)° - sin (45-30)°
= (cos 45 cos 30 + sin 45 sin 30) - (sin 45 cos 30 - cos 45 sin 30)
= [tex] [(\frac{1}{2}\sqrt{2})(\frac{1}{2} \sqrt{3}) +(\frac{1}{2}\sqrt{2})(\frac{1}{2})] - [(\frac{1}{2} \sqrt{2})(\frac{1}{2} \sqrt{3})-(\frac{1}{2} \sqrt{2})(\frac{1}{2})][/tex]
= [tex] (\frac{1}{2} \sqrt{2})(\frac{1}{2} \sqrt{3}) +(\frac{1}{2} \sqrt{2})(\frac{1}{2}) - (\frac{1}{2} \sqrt{2})(\frac{1}{2} \sqrt{3})+(\frac{1}{2}\sqrt{2})(\frac{1}{2})[/tex]
= [tex]\frac{1}{4} \sqrt{6} +\frac{1}{4} \sqrt{2} -\frac{1}{4} \sqrt{6} + \frac{1}{4} \sqrt{2}[/tex]

= [tex]\frac{1}{2} \sqrt{2}[/tex]