(1)已知cos[(π/3)-a]=根号3/3,求sin[5π/6)-a]+sin^2[(2π/3)+a]的值(2)求值:log8(3)*log9(2)+log1/2(三次根号下16)-(-3又3/8)^(-2/3)+(1.5)^-2
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![(1)已知cos[(π/3)-a]=根号3/3,求sin[5π/6)-a]+sin^2[(2π/3)+a]的值(2)求值:log8(3)*log9(2)+log1/2(三次根号下16)-(-3又3/8)^(-2/3)+(1.5)^-2](/uploads/image/z/5340410-26-0.jpg?t=%281%29%E5%B7%B2%E7%9F%A5cos%5B%EF%BC%88%CF%80%2F3%EF%BC%89-a%5D%3D%E6%A0%B9%E5%8F%B73%2F3%2C%E6%B1%82sin%5B5%CF%80%2F6%EF%BC%89-a%5D%2Bsin%5E2%5B%EF%BC%882%CF%80%2F3%EF%BC%89%2Ba%5D%E7%9A%84%E5%80%BC%282%29%E6%B1%82%E5%80%BC%EF%BC%9Alog8%283%29%2Alog9%282%29%2Blog1%2F2%28%E4%B8%89%E6%AC%A1%E6%A0%B9%E5%8F%B7%E4%B8%8B16%EF%BC%89-%EF%BC%88-3%E5%8F%883%2F8%EF%BC%89%5E%28-2%2F3%29%2B%281.5%29%5E-2)
(1)已知cos[(π/3)-a]=根号3/3,求sin[5π/6)-a]+sin^2[(2π/3)+a]的值(2)求值:log8(3)*log9(2)+log1/2(三次根号下16)-(-3又3/8)^(-2/3)+(1.5)^-2
(1)已知cos[(π/3)-a]=根号3/3,求sin[5π/6)-a]+sin^2[(2π/3)+a]的值
(2)求值:log8(3)*log9(2)+log1/2(三次根号下16)-(-3又3/8)^(-2/3)+(1.5)^-2
(1)已知cos[(π/3)-a]=根号3/3,求sin[5π/6)-a]+sin^2[(2π/3)+a]的值(2)求值:log8(3)*log9(2)+log1/2(三次根号下16)-(-3又3/8)^(-2/3)+(1.5)^-2
(1)
cos[(π/3)-a]=√3/3
(5π/6-a)-(π/3-a)=π/2
(5π/6-a)=(π/2)+(π/3-a)
sin[(5π/6-a)=sin[(π/2)+(π/3-a)]=cos(π/3-a)=√3/3
(2π/3+a)+(π/3-a)=π
sin[(2π/3+a)=sin[(π/3-a)]=±√3/3
sin^2[(2π/3+a)=sin[(π/3-a)]=1/3
原式=(√3/3)+(1/3)=(√3+1)/3
(2)
log8(3)*log9(2)+log(1/2)(三次根号下16)=[lg3/lg8][lg2/lg9]+log(1/2)[2^(4/3)
=[lg3/(3lg2)][lg2/(2lg3)]-(4/3)
=(1/6)-(8/6)= - 7/6
(-27/8)^(-2/3)+(3/2)^(-2)=[-(3/2)^3]^(-2/3)+(3/2)^2=(2/3)^2+(3/2)^2=(4/9)+(9/4)=97/36
原式= -7/6-97/36= -139/36