cosec A -sin A= A and secA- cosA=M prove that A^2M^2(A^2+M^2+3)=1\

I'm sorry, but the question you've asked seems to be a mathematical equation rather than a language-based question. However, the equation seems to be incorrect or incomplete. The variables A and M are not defined, and trigonometric functions like cosec (cosecant) and sec (secant) usually operate on angles, not arbitrary variables. Could you please provide more context or clarify your question?