Question

सिद्ध करें कि $\sin ^{2} 5^{\circ}+\sin ^{2} 85^{\circ}+\sin ^{2} 10^{\circ}+\sin ^{2} 80^{\circ}=2$.

Answer 1

Solution : बा॰प० $=\sin ^{2} 5^{\circ}+\sin ^{2}\left(90^{\circ}-5^{\circ}\right)+\sin ^{2} 10^{\circ}+\sin ^{2}\left(90^{\circ}-10^{\circ}\right)$

$=\left(\sin 5^{\circ}+\cos ^{2} 5^{\circ}\right)+\left(\sin ^{2} 10^{\circ}+\cos ^{2} 10^{\circ}\right)=1+1=2=$ दा०प०।