12求证sin3A=3sinA-4Sin^3A?求证cos3a=4cos^3a-3cosa?
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12求证sin3A=3sinA-4Sin^3A?求证cos3a=4cos^3a-3cosa?
12
求证sin3A=3sinA-4Sin^3A?
求证cos3a=4cos^3a-3cosa?
12求证sin3A=3sinA-4Sin^3A?求证cos3a=4cos^3a-3cosa?
sin3A=sin(2A+A)=sin2AcosA+cos2AsinA
=(2sinAcosA)cosA+(2cos^2A-1)sinA
=4sinAcos^2A-sinA
=4sinA(1-sin^2A)-sinA
=3sinA-4sin^3A.
cos3a=cos(2a+a)=cos2acosa-sin2asina
=(2cos^2a-1)cosa-2sin^2acosa
=2cos^3a-cosa-2(1-cos^2a)cosa
=4cos^3a-3cosa.
求证完毕!
sin3A=sin(2A+A)
=sin2AcosA+cos2AsinA
=2sinAcosAcosA+(1-2(sinA)^2)sinA
=sinA(2(cosA)^2+1-2(sinA)^2)
=sinA(2(1-(sinA)^2)+1-2(sinA)^2)
=sinA(3-4(sinA)^2)
=3sinA-4(sinA)^3
cos3...
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sin3A=sin(2A+A)
=sin2AcosA+cos2AsinA
=2sinAcosAcosA+(1-2(sinA)^2)sinA
=sinA(2(cosA)^2+1-2(sinA)^2)
=sinA(2(1-(sinA)^2)+1-2(sinA)^2)
=sinA(3-4(sinA)^2)
=3sinA-4(sinA)^3
cos3A=cos(2A+A)
=cos2AcosA-sin2AsinA
=(2(cosA)^2-1)cosA-2sinAcosAsinA
=cosA(2(cosA)^2-1-2(sinA)^2)
=cosA(2(cosA)^2-1-2(1-(cosA)^2)
=cosA(4(cosA)^2-3)
=4(cosA)^3-3cosA
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