prove : 1/cotA + cosecA = cotA - cosecA

prove : 1/cotA + cosecA = cotA - cosecA

Your formula has an error:


\frac 1 {cot(A)} + csc(A) \ne cot(A) - csc(A)


However, the following is true:


\frac 1 {cot(A) + csc(A)} = -(cot(A) - csc(A))


To prove it start by replacing the cot(A) and csc(A) functions with their sine and cosine equivalents, then simplify - for example on the left hand side multiply numerator and denominator by sin(A).