求sin^2 (10°)+cos^2(40°)+(sin10°)*(cos40°)的值
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![求sin^2 (10°)+cos^2(40°)+(sin10°)*(cos40°)的值](/uploads/image/z/972497-65-7.jpg?t=%E6%B1%82sin%5E2+%EF%BC%8810%C2%B0%EF%BC%89%2Bcos%5E2%2840%C2%B0%EF%BC%89%2B%EF%BC%88sin10%C2%B0%EF%BC%89%2A%EF%BC%88cos40%C2%B0%EF%BC%89%E7%9A%84%E5%80%BC)
求sin^2 (10°)+cos^2(40°)+(sin10°)*(cos40°)的值
求sin^2 (10°)+cos^2(40°)+(sin10°)*(cos40°)的值
求sin^2 (10°)+cos^2(40°)+(sin10°)*(cos40°)的值
求sin^2 (10°)+cos^2(40°)+(sin10°)*(cos40°)的值
因为 cos40=cos(30+10)=(√3*cos10-sin10)/2
原式=sin²10+(√3*cos10-sin10)²/4+(sin10)*(√3*cos10-sin10)/2
把cos10=√(1-sin10)代入上式,计算可得:
sin²10+(√3*cos10-sin10)²/4+(sin10)*(√3*cos10-sin10)/2=3/4
(计算过程中出现的根式与根式以及sin10的系数正好可相抵为0)