Question

已知cos45°＝√2／2,求cos²1°+...cos²89°

Answer 1

(cos1)^2+(cos2)^2+(cos3)^2+...+(cos89)^2

=[sin(90-1)]^2+[sin(90-2)]^2+...+[sin(90-44)]^2+(cos45)^2+(cos46)^2+...+(cos89)^2

=(sin89)^2＋(cos89)^2+(sin88)^2+(cos88)^2+...+(sin46)^2+(cos46)^2+(cos45)^2

=1+1+...+1(88/2=44个1）＋(cos45)^2

=44+（√2/2）^2

=44+1/2

=89/2