4SINA B 2-COS2C=7 2
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cos2A+cos2B=2cos(A+B)cos(A-B)1+cos2C=2(cosC)^2cos(A+B)=-cosC-cosCcos(A-B)=(cosC)^2所以cosC=0或-cos(A-B)
(1)因为cos2C=cos(C+C)=(cosC)平方-(sinC)平方=-3/4(cosC)平方+(sinC)平方=1得(sinC)平方=7/8所以,sinC=根号14/4(2)
cos2C=-3/4,——》2cos^2C-1=-3/4,——》cosC=v2/4,sinC=v(1-cos^2C)=v14/4,由正弦定理:c/sinC=a/sinA=b/sinB,c=2a,——》
cos2C=1-2sin^2C=-3/4则sin^2C=(1+3/4)/2=7/8sinC=√14/4当c=2a且b=3√7时,由cosC=√(1-sin^2C)=√2/4所以在三角形中,由余弦定理得
cos2C=-1/4所以cos2c=1-2(sinc)^2=-1/4可得sinc=+—根号10/4又因为角c为三角形内角所以正弦值是正数所以sinc=根号10/4
△ABC中,tanA,tanB是3x+8x-1=0的两个实数根,可得tanA+tanB=-83,tanAtanB=-13,所以tan(A+B)=tanA+tanB1-tanAtanB=-8343=-2
4cos²C/2-cos2C=7/22(1+cosC)-2cos²C+1=7/24cos²C-4cosC+1=0(2cosC-1)²=0cosC=1/2C=60
∵cos2c=1-sin^2 C ∴sin C=√10 /42)Sin A=1/2 sin C = √10&n
cos2C=-1/4所以cos2c=1-2(sinc)^2=-1/4可得sinc=+—根号10/4又因为角c为三角形内角所以正弦值是正数所以sinc=根号10/4再问:其实这道题我已经做出来了、不过还
由正弦定理得a/sinA=b/sinB,因为acosA=bcosB,所以sinAcosB-cosAsinB=sin(A-B)=0,所以∠A=∠B.cos2A+cos2B-cos2C=2cos2A-co
超简单~的思路一般都是联系条件(三角形)那么就把“大角化小角,一步一步慢慢走咯(柴)”.1-2sin^2A+1-2sin^2B-1+2sin^2C=1得sin^2A+sin^2B=sin^2C在用上正
sin²2C+sin2C×sinC+cos2C=1,4sin²C*cos²C+2sin²CcosC+1-2sin²C=1,2cos²C+co
4sin^2(A+B)-cos2C=2[1-cos(A+B)]-(2cos^2C-1)=7/2,4cos^2C-4cosC+1=0cosC=1/2,C=60度a+b=5,a^2+2ab+b^2=25,
∵ab≤(a+b)^2/4=25/4ab最大值25/4<9CosC=(a^2+b^2-c^2)/2ab=[(a+b)^2-c^2-2ab]/2ab=(25-7-2ab)/2ab=(18-2ab)2ab
单独求第二问,根据正弦定理,得a/sinA=c/sinC,∴c=asinC/sinA=4,cos2C=2cos²-1,∴cosC=√6/4或-√6/4,cosC=(a²+b
cos2C=2cos^2C-1=-3/4cos^2C=1/8cosC=√2/4余弦定理√2/4=(b^2+a^2-c^2)/2abc=2a√2/4=(63+a^2-4a^2)/6√7a2a^2+√14
4sin²(A+B/2)-cos2C=2-2cos(A+B)-(2cos²C-1)=3+2cosC-2cos²C=7/2所以cosC=1/2,所以∠C=60°cosC=a
/>4sin²[(A+B)/2-cos2C=7/2,2(1-cos(A+B))-(2cos²C-1)=7/2,2(1+cosC)-(2cos²C-1)=7/2,2+2co
sin(A+B)=cos2Csin(180-C)=1-2sin²CsinC=1-2sin²C2sin²C+sinC-1=0(sinC+1)(2sinC-1)=0C是内角则
a=1,c=根号7,则解法如下:∵4sin^2(A+B)/2)-cos2C=7/24sin^2[(180°-C)/2]-cos2C=7/24sin^2(90°-C/2)-cos2C=7/24cos^2