化简:sin^A*sin^A+sin(A-60°)*sin(A-60°)+sin(A+60°)*

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/07 03:41:25
化简:sin^A*sin^A+sin(A-60°)*sin(A-60°)+sin(A+60°)*

化简:sin^A*sin^A+sin(A-60°)*sin(A-60°)+sin(A+60°)*
化简:sin^A*sin^A+sin(A-60°)*sin(A-60°)+sin(A+60°)*

化简:sin^A*sin^A+sin(A-60°)*sin(A-60°)+sin(A+60°)*
sin^2 A + sin^2 (A + 60 °) + sin^2 (A - 60 °)
= sin^2 A + (1 - cos2 (A + 60 °))/2 + (1 - cos2 (A - 60 °))/2
= sin^2 A + 1 -
1/2*2 cos (2 A + 120 ° + 2 A - 120 °)/2 cos (
2 A + 120 ° - 2 A + 120 °)/2
= sin^2 A + 1 - cos2Acos120
= sin^2 A + 1 + 1/2 cos2A
= sin^2 A + 1 + cos^2 A - 1/2
= 3/2