Notăm cu S,suma
[tex]S=sin^2 1+sin^2 2+...+sin^2 90[/tex]
Cunoastem doua proprietăti ale functiilor trigonometrice
[tex]sin(90- \alpha )=cos \alpha [/tex]
[tex]cos(90- \alpha )=sin \alpha [/tex]
[tex]sin^2x+cos^2x=1[/tex]
[tex]sin^2 \alpha =cos^2(90- \alpha )[/tex]
Suma devine
[tex]S=sin^2 1+sin^2 2+...+sin^2 90
S=cos^289+cos^288+.................cos^20[/tex]
Dacă adunăm cele doua relatii
[tex]2S=(sin^21+cos^21)+(sin^22+cos^22)+..............................
+(sin^289+cos^289)+sin^290+cos^20
2S=89+1+1
2S=91
S=91/2[/tex]
[tex]SIN^21+COS^21=1 ETC.
sin^22+cos^22=1[/tex]
