Let x=sin A
The equation is "equivalent" to:
[tex] x^{2} [/tex]-1 over x+1 = x-1
Multiplying x+1 to both sides gives:
[tex] x^{2} [/tex]-1=(x+1)(x-1)
Since [tex] a^{2} [/tex]-[tex] b^{2} [/tex]=(a+b)(a-b),
Therefore,
[tex] x^{2} [/tex]-1=[tex] x^{2} [/tex]-1