已知sin(2a+b)=5sinb,求证2tan(a=b)=3tana

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已知sin(2a+b)=5sinb,求证2tan(a=b)=3tana
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已知sin(2a+b)=5sinb,求证2tan(a=b)=3tana
已知sin(2a+b)=5sinb,求证2tan(a=b)=3tana

已知sin(2a+b)=5sinb,求证2tan(a=b)=3tana
5sin[(A + B) - A] = sin[(A + B) + A]
左边 = 5sin(A + B)cosA - 5cos(A + B)sinA
右边 = sin(A + B)cosA + cos(A + B)sinA ,移项得:
4sin(A + B)cosA = 6cos(A + B)sinA
两边除以 2cosAcos(A + B) 即得:
2tan(A+B)=3tanA