题目内容：

证明：tanAsinA/(tanA-sinA)=(tanA+sinA)/tanAsinA
是证明题.

优质解答

tanAsinA/(tanA-sinA)
=sinA/cosA*sinA/(sinA/cosA-sinA)
=sinA/cosA*sinA*(1/cosA+1)/{(1/cosA+1)*(sinA/cosA-sinA)}
=sinA*sinA(1/cosA+1/cos^2A)/{sinA*(1/cos^2A-1)}
=sinA*sinA(1/cosA+1/cos^2A)*cosA/(sinA*sin^2A/cosA)
=sinA(1+1/cosA)/tanAsinA
=(tanA+sinA)/tanAsinA