tan(A+B)=2tanB 证明3sinA=sin(A+2B)
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tan(A+B)=2tanB 证明3sinA=sin(A+2B)
tan(A+B)=2tanB 证明3sinA=sin(A+2B)
tan(A+B)=2tanB 证明3sinA=sin(A+2B)
sin(A+2B)=sin(A+B)cosB+cos(A+B)sinB=tan(A+B)cos(A+B)cosB+cos(A+B)cosBtanB=2tanBcos(A+B)cosB+tanBcos(A+B)cosB=3sinBcos(A+B)
再对右边积化和,得
sin(A+2B)=3sin(A+2B)/2+3sin(-A)/2
移项得,3sinA/2=sin(A+2B)/2
所以
3sinA=sin(A+2B)