Áp dụng vào bài ta được:

`sin^2(15^o)+cos^2(15^o)=1`

`->((\sqrt{6}-\sqrt{2})/4)^2+cos^2(15^o)=1`

`->cos^2(15^o)=1-((\sqrt{6}-\sqrt{2})/4)^2`

`->cos^2(15^o)=1-(6-2\sqrt{6}*\sqrt{2}+2)/16`

`->cos^2(15^o)=1-(2-\sqrt{3})/4`

`->cos^2(15^o)=(4-2+\sqrt{3})/4`

`->cos^2(15^o)=(2+\sqrt{3})/4` 

`->cos^2(15^o)=(8+8\sqrt{3})/16`

`->cos^2(15^o)=(6+2\sqrt{6}*\sqrt{2}+2)/4^2`

`->cos^2(15^o)=((\sqrt{6}+\sqrt{2})/4)^2`

`->cos(15^o)=(\sqrt{6}+\sqrt{2})/4` hoặc `cos(15^o)=-(\sqrt{6}+\sqrt{2})/4`

Vậy: `...`