נושא : שימוש בזהויות ( s i n α + c o s α ) 2 = 1 + 2 sin α cos α ? s i n 2 α + 2 c o s α sin α + c o s 2 α = 1 + 2 sin α cos α c o s 2 + s i n 2 = 1 1 + 2 sin α cos α = 2 sin α cos α {\displaystyle {\begin{aligned}&(sin\alpha +cos\alpha )^{2}=1+2\sin \alpha \cos \alpha ?\\&sin^{2}\alpha +2cos\alpha \sin \alpha +cos^{2}\alpha =1+2\sin \alpha \cos \alpha \\&\color {blue}cos^{2}+sin^{2}=1\\&1+2\sin \alpha \cos \alpha =2\sin \alpha \cos \alpha \\\end{aligned}}}
