<prompt> Tafuta jumla ya pembe zote x katika 0circ, 360circ zinazokidhisin5 x - cos5 x frac1cos x - frac1sin x.  <response>: Tunaweza kuandika upande wa kulia kamasin5 x - cos5 x fracsin x - cos xsin x cos x,hivyo sin x cos x sin5 x - cos5 x dhambi x - cos x, audhambi x cos x sin5 x - cos5 x - sin x - cos x 0.Tunaweza kuainisha ili kupatadhambi x cos x dhambi x - cos xdhambi4 x dhambi3 x cos x dhambi2 x cos2 x sin x cos 3 x cos4 x - sin x - cos x 0.Tunaweza kuandikaanzaaligndhambi4 x dhambi3 x cos x dhambi2 x cos2 x dhambi x cos3 x cos4 x dhambi4 x 2 dhambi2 x cos2 x cos4 x - dhambi2 x cos2 x dhambi x cos x dhambi2 x cos2 x dhambi2 x cos2 x2 - dhambi2 x cos2 x dhambi x cos x dhambi2 x cos2 x 1 dhambi x cos x - dhambi2 x cos2 x,mwishoalignhivyodhambi x cos x dhambi x - cos x1 dhambi x cos x - sin2 x cos2 x - dhambi x - cos x 0 .Hebu p sin x cos x, hivyop sin x - cos x1 p - p2 - sin x - cos x 0.Kishadhambi x - cos xp p2 - p3 - 1 0, ni vipengele vipi- dhambi x - cos xp - 12 p 1 0.Tangup dhambi x cos x frac12 2 sin x cos x frac12 sin 2x le frac12,thamani p haiwezi kamwe kuwa 1 au -1. Kwa hivyo, sin x cos x, au tan x 1. The suluhu pekee katika 0circ, 360circ ni 45circ na 225circ, na jumla yao ni 270circ. 