Bereken [math](\sin(15°)+\cos(15°)^2+(\sin(30°)+\cos(30°)^2+(\sin(45°)+\cos(45°)^2+(\sin(60°)+\cos(60°)^2+(\sin(75°)+\cos(75°)^2+(\sin(90°)+\cos(90°)^2[/math]
omdat [math]\sin^2(\alpha)+\cos^2(\alpha)=1\; en\; (A+B)^2=A^2+2AB+B^2\;en\;2\sin(\alpha)\cos(\alpha)=\sin(2\alpha)[/math] is bovenstaande uitdrukking gelijk aan [math](1+\sin(30°))+(1+\sin(60°))+(1+\sin(90°))+(1+\sin(120°))+(1+\sin(150°))+(1+\sin(180°))[/math][br][math]6+\frac{1}{2}+\frac{\sqrt{3}}{2}+1+\frac{\sqrt{3}}{2}+\frac{1}{2}=8+\sqrt{3}[/math][br]