(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：2024/05/12 04:40:46

(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.

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