数学推理sin10+cos40+sin10cos40=3/4,sin6+c0s36+sin6cos36=3/4猜想规律
答案:1 悬赏:70
解决时间 2021-02-17 10:49
- 提问者网友：你给我的爱
- 2021-02-16 20:29
数学推理sin10+cos40+sin10cos40=3/4,sin6+c0s36+sin6cos36=3/4猜想规律
最佳答案
- 二级知识专家网友：鸽屿
- 2021-02-16 21:47
题目有误
sin^2 10+cos^2 40+sin 10cos40=3/4
sin^2 6+cos^2 36+sin6 cos36=3/4
(sina)^2+(cos(a+30))^2+sinacos(a+30)=3/4
证明:
(sina)^2+[cos(a+30)]^2+sinacos(a+30)
=(1-cos2a)/2+[1+cos(2a+60)]/2+sina
(cosacos30-sinasin30)
=1-(1/2)(1-2(sina)^2)+(1/2)(cos2acos60-sin2asin60)+(√3/2)sinacosa-(1/2)(sina)^2
=1-(1/2)(1-2(sina)^2)+(1/4)(1-2(sina)^2)-(√3/4)sin2a+(√3/4)sin2a-(1/2)(sina)^2
=1-1/2+1/4
=3/4
sin^2 10+cos^2 40+sin 10cos40=3/4
sin^2 6+cos^2 36+sin6 cos36=3/4
(sina)^2+(cos(a+30))^2+sinacos(a+30)=3/4
证明:
(sina)^2+[cos(a+30)]^2+sinacos(a+30)
=(1-cos2a)/2+[1+cos(2a+60)]/2+sina
(cosacos30-sinasin30)
=1-(1/2)(1-2(sina)^2)+(1/2)(cos2acos60-sin2asin60)+(√3/2)sinacosa-(1/2)(sina)^2
=1-(1/2)(1-2(sina)^2)+(1/4)(1-2(sina)^2)-(√3/4)sin2a+(√3/4)sin2a-(1/2)(sina)^2
=1-1/2+1/4
=3/4
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