高一三角函数已知三角形ABC的三
分析:
∵三角形ABC的三个内角A,B,C成等差数列(A<B<C)
∴2B=A+C
∵A+B+C=180°
∴A+C=120°; B=60°
∵sinA,sinB,3sinC成等比数列
∴(sin60°)^2=3*sinA*sinC =3/4
∴sinA*sinC =1/4
∵sinA*sinC
=(-1/2)*[cos(A+C)-cos(A-C)]
=(-1/2)*[cos120°-cos(A-C)]
=(-1/2)*[(-1/2)-cos(A-C)]
∵sinA*sinC =1/4
∴(-1/2)*[(-1/2)-cos(A-C)]=1/4
∴cos(A-C)=0
∴A-C=90°或C...全部
分析:
∵三角形ABC的三个内角A,B,C成等差数列(A<B<C)
∴2B=A+C
∵A+B+C=180°
∴A+C=120°; B=60°
∵sinA,sinB,3sinC成等比数列
∴(sin60°)^2=3*sinA*sinC =3/4
∴sinA*sinC =1/4
∵sinA*sinC
=(-1/2)*[cos(A+C)-cos(A-C)]
=(-1/2)*[cos120°-cos(A-C)]
=(-1/2)*[(-1/2)-cos(A-C)]
∵sinA*sinC =1/4
∴(-1/2)*[(-1/2)-cos(A-C)]=1/4
∴cos(A-C)=0
∴A-C=90°或C-A=90°
∵A+C=120°
∴A=105°,B=60°,C=15°或A=15°,B=60°,C=105°
。
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