已知α、β为锐角, 3sin平方α 2sin平方β=1, 3sin2α-2sin2β=0.求证：α 2β=π/2.已知α、β为锐角, 3sin平方α+2sin平方β=1, 3sin2α-2sin2β=0.求证：α+2β=π/2.
热心网友
证明:由3(sinα)^2+2(sinβ)^2=1得 3(sinα)^2=1-2(sinβ)^2=cos2β (1)由3sin2α-2sin2β=0得 3sinαcosα=sin2β (2)(2)/(1)得:cotα=tan2β 即:tan(π/2-α)=tan2β (3)再由(1)知道:2β为锐角 ,所以π/2-α=2β 于是α+2β=π/2