Prove that- cosA / cosecA - 1 + sinA / 1 - cotA = sinA + cosA?

Answer 1

Can't be done, because this isn't true. Let A=π/2. Then the left hand side of the equation becomes 0/1-1+1/1-0, which is zero, and the right hand side is 1. Of course, perhaps you meant to write instead cos A/csc A - (1 + sin A)/(1 - cot A), in which case the identity still does not hold for A=π/2, because 0/1-(1+1)/(1-0)=-2, which still is not equal to 1. Thus this trigonometric identity is not true and as such cannot be proven.

Answer 2

cos A/(cosecA-a million) +sinA/(a million-cotA) = (cosA(a million-cotA)+sin A(cosecA-a million) )/(cosecA-a million) (a million-cotA) = (cosA-(cosA)^2/sin A+a million-sinA)/(cosecA-a million) (a million-cotA) =(cosAsinA - (cosA)^2 - (sinA)^2+sinA)/(sinA(cosecA-a million) (a million-cotA)) =(cosAsinA-a million+sinA)/(sinA(cosecA-a million) (a million-cotA)) in here some fee could exchange