<prompt> Kokotoa:sin fracpi12 sin frac3pi12 sin frac5pi12 sin frac7pi12 sin frac9pi12 sin frac11pi12.  <response>: Ona kwamba tatizo lina jozi tatu za fomu sin theta sinpi - theta. Fomula ya jumla kwa bidhaa inatoaanzaalignsin fracpi12 sin frac11pi12 2 sin fracpi2 cos frac5pi12 2 cos frac5pi12, sin frac3pi12 sin frac9pi12 2 sin fracpi2 cos fracpi4 sqrt2, sin frac5pi12 sin frac7pi12 2 sin fracpi2 cos fracpi12 2 cos fracpi12.endalignKutumia fomula ya jumla-kwa-bidhaa kwa mara nyingine tenaanzaalign sin fracpi12 sin frac3pi12 sin frac5pi12 sin frac7pi12 dhambi frac9pi12 dhambi frac11pi12 sqrt2 2 Bigcos frac5pi12 cos fracpi12 Big sqrt2 4 cos fracpi4 cos fracpi6 sqrt2 4 cdot frac1sqrt2 cdot fracsqrt32 sqrt2 sqrt6.mwishopanga 