[tex]sin15^o=\frac{\sqrt6-\sqrt2}{4}[/tex]
[tex]sin^215^o+cos^215^o=1[/tex]
[tex]\left(\frac{\sqrt6-\sqrt2}{4}\right)^2 +cos^215^o=1[/tex]
[tex]\frac{6-2\sqrt{12}+2}{16} +cos^215^o=1[/tex]
[tex] cos^215^o=1-\frac{8-2\sqrt{12}}{16}[/tex]
[tex] cos^215^o=\frac{16-8+2\sqrt{12}}{16}[/tex]
[tex] cos^215^o=\frac{8+2\sqrt{12}}{16}[/tex]
[tex] cos^215^o=\frac{6+2\sqrt{12}+2}{16}[/tex]
[tex] cos^215^o=\frac{(\sqrt6+\sqrt2)^2}{16}[/tex]
[tex] cos15^o=\sqrt{\frac{(\sqrt6+\sqrt2)^2}{16}}[/tex]
[tex] cos15^o=\frac{\sqrt6+\sqrt2}{4}[/tex]
[tex]sin75^o=sin(90^o-15^o)=cos15^o=\frac{\sqrt6+\sqrt2}{4}[/tex]
