(15) If I look for the common denominator I get
{cos A(1 - cot A) + sin A(1 - tan A)} / {1 - cot A - tan A + tan A*cot A}
But I don't seem to see any expressions that can be simplified from here. I am awkwardly changing the cos A to sin A*cot A, or cot to 1/tan, but getting more numerators and denominators. I can only see that the tan A*cot A at the end can be changed to +1, as tan A*(1/tan A) = (tan A)/(tan A).
Till now the questions have had mostly recognizable identities, such as 1 - cos^2 A, or sec^2 - 1, but for the first time I am seeing similar expressions to these but without the second power, but don't know how to manipulate them.
(18) Likewise with the common denominator I have
(sin^2 A + 1 + 2*cos A + cos^2 A) / (sin A + sin A*cos A)
But my thoughts again would lead me to change the sin^2 A into 1 - cos^2 A, or go all obscure with (1/sec^2 A) * (cos A*tan A). Can you go from here?
But thanks for reading thus far.