已知a,b都是锐角,且满足sina–sinb=-05,cosa–cosb=05,求tan(
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解决时间 2021-11-25 14:35
- 提问者网友：wodetian
- 2021-11-25 07:16
已知a,b都是锐角,且满足sina–sinb=-05,cosa–cosb=05,求tan(
最佳答案
- 五星知识达人网友：狂恋
- 2021-11-25 08:01
sinA-sinB=-0.5
sin^2A+sin^2B-2sinAsinB=0.25..............(1)
cosA-cosB=0.5
cos^2A+cos^2B-2cosAcosB=0.25...........(2)
(1)+(2)：
(sin^2A+cos^2A)+(sin^2B+cos^2B)-2(sinAsinB+cosAcosB)=0.5
1+1-2cos(A-B)=0.5
cos(A-B)=3/4
sin(A-B)=√[1-cos^2(A-B)]
=√[1-(3/4)^2]
=√7/4
tan(A-B)=sin(A-B)/cos(A-B)
=(3/4)/(√7/4)
=3√7/7
sin^2A+sin^2B-2sinAsinB=0.25..............(1)
cosA-cosB=0.5
cos^2A+cos^2B-2cosAcosB=0.25...........(2)
(1)+(2)：
(sin^2A+cos^2A)+(sin^2B+cos^2B)-2(sinAsinB+cosAcosB)=0.5
1+1-2cos(A-B)=0.5
cos(A-B)=3/4
sin(A-B)=√[1-cos^2(A-B)]
=√[1-(3/4)^2]
=√7/4
tan(A-B)=sin(A-B)/cos(A-B)
=(3/4)/(√7/4)
=3√7/7
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