# Prove the given identity using the shortest method possible [duplicate]

Prove the given identity. $$\left(\sin\frac{9\pi}{70}+\sin\frac{29\pi}{70}-\sin\frac{31\pi}{70}\right)\left(\sin\frac{\pi}{70}-\sin\frac{11\pi}{70}-\sin\frac{19\pi}{70}\right)=\frac{\sqrt{5}-4}{4}$$

Please provide the shortest method possible. I didn't get any idea to start the solution

• i would multiply out these terms – Dr. Sonnhard Graubner Mar 25 '17 at 11:51
• @Dr.SonnhardGraubner, I guess it would be more complex. – Aryabhatta Mar 25 '17 at 11:56
• @Dr. Sonnhard Graubner, is it possible to use Euler identity? – Aryabhatta Mar 25 '17 at 12:00
• An answer is given in math.stackexchange.com/questions/1895204/… – mlc Mar 25 '17 at 17:40
• @divx Thank you for pointing out that I put the above info in the wrong place. – mlc Mar 25 '17 at 17:42