Question

Sin patrat 20°+ sin patrat 110°

Answer 1

   
$\displaystyle\\ \sin^220^o+\sin^2110^o=?\\ \text{Unghiul de }110^o\text{ este obtuz}\\ \text{Calculam suplementul acestui unghi:}\\ 180^o-110^o=70^o\\ \Longrightarrow~~\sin^2110^o = \sin^2(180^o-70^o)=\sin^2 70^o\\\\ \sin^220^o+\sin^2110^o=\sin^220^o+\sin^270^o=?\\ \text{Unghiul de }70^2\text{ este complementar cu unghiul de }20^o. \\20^0+70^o=90^o\\ \Longrightarrow~~\sin^270^o=\cos^2(90^o-70^o)=\cos^220^o\\\\ \sin^220^o+\sin^2110^o=\sin^220^o+\sin^270^o=\sin^220^o+\cos^220^o=\boxed{\bf 1}$