Question

sa se arate ca sin patrat de un grad +sin patrat de 2 grade +...+ sin patrat de 90 de grade = 91/2

Answer 1

sin²1°+sin²89°=sin²1°+cos²1°=1
sin²2°+sin²88°=sin²2°+cos°2°=1
..........................................................
sin²44°+sin²46°=sin²44°+cos²44°=1
sin²45°=(1/√2)²=1/2
sin²90°=1²=1
 toata suma =1+1+...+1 (44de 1)+1/2+1=44+3/2=(88+3)/2=91/2
C.C.T.D.
as simple as that!