△ABC中,内角A,B,C对应的变为a,b,c,且A=80°,a^2=b(b+c),则角C度数为
△ABC中,内角A,B,C对应的变为a,b,c,且A=80°,a^2=b(b+c),则角C度数为
如题.
三角函数的积化和差与和差化积.
如题.
三角函数的积化和差与和差化积.
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a^2=b(b+c),
a^2=b^2+bc,
而,a=2R*sinA,b=2R*sinB,c=2R*sinC,
sin^2A=sin^2B+sinB*sinC,
sin^2A-sin^2B=sinB*sinC,
(sinA+sinB)(sinA-sinB)=sinB*sinC,
2*sin(A+B)/2*cos(A-B)/2*2*cos(A+B)/2*sin(A-B)/2=sinB*sinC,
sin(A+B)*sin(A-B)=sinB*sinC,
而,A+B+C=180,A+B=180-C,
sin(A+B)=sinC,
即有,sin(A-B)=sinB,
A-B=B,
A=2B ,A=80
B=40
C=180-80-40=60
a^2=b^2+bc,
而,a=2R*sinA,b=2R*sinB,c=2R*sinC,
sin^2A=sin^2B+sinB*sinC,
sin^2A-sin^2B=sinB*sinC,
(sinA+sinB)(sinA-sinB)=sinB*sinC,
2*sin(A+B)/2*cos(A-B)/2*2*cos(A+B)/2*sin(A-B)/2=sinB*sinC,
sin(A+B)*sin(A-B)=sinB*sinC,
而,A+B+C=180,A+B=180-C,
sin(A+B)=sinC,
即有,sin(A-B)=sinB,
A-B=B,
A=2B ,A=80
B=40
C=180-80-40=60
1年前
5
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