We work with the left side:



Let s = sin(A) 
Let c = cos(A)



Factor numerator as the sum of two cubes
and the trinomial in the denominator



Cancel the (s+c)'s





Replace s and c by what we let them be above:



By a well known identity, looking at the first
and third terms, the numerator becomes



We break that into two fractions:



In the second fraction, divide every term,
top and bottom by sin(A)



Cancel the sin(A)'s in the top, and the sin(A)'s in the bottom





By using a well-known identity for cot(A):



Edwin