Cos 5pi/12-cos pi/12

[latex]cos \frac{5 \pi }{12} -cos \frac{ \pi }{12} =-2sin \frac{\frac{5 \pi }{12}+\frac{ \pi }{12}}{2} *sin \frac{\frac{5 \pi }{12}-\frac{ \pi }{12}}{2} =-2sin{ \frac{ \pi }{4} }*sin \frac{ \pi }{6}=[/latex][latex]=-2* \frac{ \sqrt{2} }{2} * \frac{1}{2} =- \frac{ \sqrt{2} }{2} [/latex]