1.若cos(π/6-α)=(√3)/3,则cos(5π/6+α)-sin^2(α-π/6)的值是多少?(详解,注:√3
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1.若cos(π/6-α)=(√3)/3,则cos(5π/6+α)-sin^2(α-π/6)的值是多少?(详解,注:√3表示根号3,sin^2(α-π/6)表示sin(α-π/6)的平方)
2.已知A、B、C、为△ABC的三个内角,且∠A=60°,则sin(2A+B+C)的值为多少?(详解)
3.已知sinβ=1/3,sin(α+β)=1,则sin(2α+β)的值为多少?(详解)
4.已知sin195°=a,求tan165°的值.(详解)
2.已知A、B、C、为△ABC的三个内角,且∠A=60°,则sin(2A+B+C)的值为多少?(详解)
3.已知sinβ=1/3,sin(α+β)=1,则sin(2α+β)的值为多少?(详解)
4.已知sin195°=a,求tan165°的值.(详解)
1.cos(5π/6+α)-sin^2(α-π/6)
=-cos{π-(5π/6+α)}-{1-cos^2(α-π/6)}
=-cos(π/6-α)-1+cos^2(α-π/6)
=-√3/3-1+1/3
=-(2+√3)/3
2.sin(2A+B+C)=sin(A+π)=-sinA=-sin60°=-√3)/2
3.因为sin(α+β)=1,所以α+β=π/2+2Kπ.(K为整数)
所以α=π/2+2Kπ-β
所以sin(2α+β)=sin(α+α+β)=sin(π/2+2Kπ-β+π/2+2Kπ)=
sin(π+4Kπ-β)=sin(π-β)=sinβ=1/3.
4.sin195°=sin(180°+15°)=-sin15°=a
所以sin15°=-a
tan165°=tan(180°-15°)=-tan15°
=-sin15°/cos15°
=-sin^2(15°)/(sin15°*cos15°)
=-sin^2(15°)/(1/2*sin30°)
=-4sin^2(15°)
=-4a^2
=-cos{π-(5π/6+α)}-{1-cos^2(α-π/6)}
=-cos(π/6-α)-1+cos^2(α-π/6)
=-√3/3-1+1/3
=-(2+√3)/3
2.sin(2A+B+C)=sin(A+π)=-sinA=-sin60°=-√3)/2
3.因为sin(α+β)=1,所以α+β=π/2+2Kπ.(K为整数)
所以α=π/2+2Kπ-β
所以sin(2α+β)=sin(α+α+β)=sin(π/2+2Kπ-β+π/2+2Kπ)=
sin(π+4Kπ-β)=sin(π-β)=sinβ=1/3.
4.sin195°=sin(180°+15°)=-sin15°=a
所以sin15°=-a
tan165°=tan(180°-15°)=-tan15°
=-sin15°/cos15°
=-sin^2(15°)/(sin15°*cos15°)
=-sin^2(15°)/(1/2*sin30°)
=-4sin^2(15°)
=-4a^2
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