<prompt> Je, ni nambari ngapi chanya n chini ya au sawa na 1000 ni sin ticos tnsin nticos nttrue kwa t yote halisi?  <response>: Kumbuka kwamba anzaalignsin ticos tnkushotocoskushotopiover2-tkuliaidhambikushotopiover2-tkuliakulian cosnkushotopiover2-tright isinnkushotopiover2-tkulia cosleftnpiover2-ntrightisinleftnpiover2-ntright,endalignna hiyo displaystylesin nticos nt cosleftpiover2-ntrightisinleftpiover2-ntright. Kwa hivyo hali iliyopewa ni sawa na cosleftnpiover2-ntright coskushotopiover2-ntkulia quad rm na quadsinleftnpiover2-ntright sinleftpiover2-ntright.Kwa ujumla, cosalphacosbeta na sinalphasinbeta if and only ikiwa alpha -beta2pi k. Hivyo npiover2-nt-piover2nt2pi k,ambayo inatoa n4k1. Kwa sababu 1le nle1000, inahitimisha kuwa 0le kle 249, kwa hivyo kuna thamani za 250 za n ambazo zinakidhi masharti yaliyotolewa. 