Question

Să se arate că: sin^2 1°+ sin^2 2° +...+ sin^2 90°=91/2

Answer 1

(sin 1)^2+(sin 2)^2+...+(sin 88)^2+(sin 89)^2+(sin 90)^2= 
=((sin 1)^2+(sin 89)^2)+((sin 2 )^2+( sin 88)^2+...+ 
+((sin 44)^2+(sin 46)^2)+(sin 45)^2+(sin 90)^2= 
1+1+....+1+(sin 45)^2+1=45+(1/2)=91/2