根号2*sin(π/4-x)+根号6*sin(π/4+x)的化简结果是
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/22 09:56:18
根号2*sin(π/4-x)+根号6*sin(π/4+x)的化简结果是
(根号2)/4*sin(π/4-x)+(根号6)/4*cos(π/4-x)
=√2/2[1/2sin(π/4-x)+√3/2*cos(π/4-x)]
=√2/2[cos60°sin(π/4-x)+sin60°cos(π/4-x)]
= √2/2 sin(105°-x)
或者:
(根号2)/4*sin(π/4-x)+(根号6)/4*cos(π/4-x)
=√2/2[1/2sin(π/4-x)+√3/2*cos(π/4-x)]
=√2/2[sin30°sin(π/4-x)+cos30°cos(π/4-x)]
= √2/2 cos(x-15°)
知识点:
sin(A+B)=cosAsinB+sinAcosB.
sin(A-B)=sinAcosB-cosAsinB.
cos(A-B)=sinAsinB+cosAcosB.
cos(A+B)=cosAcosB-sinAsinB
=√2/2[1/2sin(π/4-x)+√3/2*cos(π/4-x)]
=√2/2[cos60°sin(π/4-x)+sin60°cos(π/4-x)]
= √2/2 sin(105°-x)
或者:
(根号2)/4*sin(π/4-x)+(根号6)/4*cos(π/4-x)
=√2/2[1/2sin(π/4-x)+√3/2*cos(π/4-x)]
=√2/2[sin30°sin(π/4-x)+cos30°cos(π/4-x)]
= √2/2 cos(x-15°)
知识点:
sin(A+B)=cosAsinB+sinAcosB.
sin(A-B)=sinAcosB-cosAsinB.
cos(A-B)=sinAsinB+cosAcosB.
cos(A+B)=cosAcosB-sinAsinB
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