在△ABC中,A,B,C,所对的边分别为a,b,c,,tanC=答:(1)tanC=sinC/cosC=(sinA+sinB)/(cosA+cosB),∴sinC(cosA+cosB)=cosC(sinA+sinB),∴sinCcosB-cosCsinB=sinAcosC-cosAsinC,∴sin(C-B)=sin(A-C),∴C-B=A-C或C-B+A-C=(2k+1)π,k∈Z,∴C=π/3(后者不可能).A+B=2π/3,sin(B-A)=cosC=1/2,∴B-A=π/6,A=π/4...
矩阵A,B,且AB=BA ,怎么证明(A+B)^n = C(n,0)A^n+C(n,1)A^(n-1)B+C...答:(A+B)= (C(k,0)A^k+C(k,1)A^(k-1)B+C(k,2)A^(k-2)B^2+...+C(k,k)B^k)(A+B)=C(k,0)A^(k+1)+(C(k,1)+C(k,0))A^kB+C(k,2)A^(k-2)B³+...+ (C(k,k)+C(k,k-1))AB^k + C(k,k)B^(k+1)=C(k+1,0)A^(k+1)+C(k+1,1)...
在三角形ABC中,角A,B,C的对边分别为a,b,c,且满足2c-b/a=cosB/cosA_百 ...答:在△ABC中,角A,B,C的对边a,b,c且满足(2c-b)/a=cosB/cosA (1)求A的大小 (2)若a=2√5,求△ABC面积的最大值 解:(1)设a/sinA=b/sinB=c/sinC=k (2c-b)/a=(2ksinC - ksinB)/(ksinA)=(2sinC-sinB)/sinA ∴(2sinC-sinB)/sinA=cosB/cosA 即sinAcosB=(2sinC-sinB)cosA=...