(cos^2)15°-(sin^2)15等于多少
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 05:53:07
![(cos^2)15°-(sin^2)15等于多少](/uploads/image/z/1709081-17-1.jpg?t=%28cos%5E2%2915%C2%B0-%28sin%5E2%2915%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91)
(cos^2)15°-(sin^2)15等于多少
(cos^2)15°-(sin^2)15等于多少
(cos^2)15°-(sin^2)15等于多少
这是因为:
方法一:
(cos^2)15°-(sin^2)15
=(cos15+sin15)(cos15-sin15)
=[sin(90-15)+sin15][sin(90-15)-sin15]
=(sin75+sin15)(sin75-sin15)
=2*sin(75+15)/2*cos(75-15)/2*2*cos(75+15)*sin(75-15)/2
=4*sin45*cos30*cos45*sin30
=√3/2.
方法二:
cos15°=cos(45-30)=cos45*cos30+sin45*sin30
=√2/2*√3/2+√2/2*1/2
=(√6+√2)/4.
cos^2(15)=[(√6+√2)/4]^2=(2+√3)/4,
sin15=sin(45-30)=sin45*cos30-cos45*sin30
=√2/2*√3/2-√2/2*1/2
=(√6-√2)/4.
sin^2(15)=[(√6-√2)/4]^2=(2-√3)/4.
(cos^2)15°-(sin^2)15=(2+√3)/4-(2-√3)/4
=√3/2.
cos15°=cos(45-30)=cos45*cos30+sin45*sin30 =√2/2*√3/2+√2/2*1/2 =(√6+√2)/4. cos^2(15)=[(√6+√2)/4]^2=(2+√3)/4, sin15=sin(45-30)=sin45*cos30-cos45*sin30 =√2/2*√3/2-√2/2*1/2 =(√6-√2)/4. sin^2(15)=[(√6-√2)/4]^2=(2-√3)/4. (cos^2)15°-(sin^2)15=(2+√3)/4-(2-√3)/4 =√3/2.