$\begin{array}{l}12)\,F = \dfrac{\sin a - 3\cos a}{\cos a + 2\sin a}\qquad (\tan a = -3)\\ \to F = \dfrac{\dfrac{\sin a}{\cos a} - 3}{1 + 2\dfrac{\sin a}{\cos a}}\\ \to F = \dfrac{\tan a -3 }{1 + 2\tan a}\\ \to F = \dfrac{-3 -3}{1 + 2.(-3)} = \dfrac{6}{5}\\ 13)\, G = \dfrac{2\cos^2a + \sin a\cos a - \sin^2a}{\sin^2a + 3\cos^2a - 4}\qquad (\cot a = 2)\\ \to G = \dfrac{2\left(\dfrac{\cos a}{\sin a}\right)^2 + \left(\dfrac{\cos a}{\sin a}\right) - 1}{1 + 3\left(\dfrac{\cos a}{\sin a}\right)^2 - \dfrac{4}{\sin^2a}}\\ \to G = \dfrac{2\cot^2a + \cot a - 1}{1 + 3\cot^2a - 4(\cot^2a + 1)}\\ \to G = \dfrac{2\cot^2a + \cot a - 1}{-\cot^2a -3}\\ \to G = \dfrac{2.2^2 + 2 -1}{-2^2 -3} = - \dfrac{9}{7}\\ 14)\, B = \dfrac{2\sin a - 3\cos a}{\sin a + \cos a}\qquad (\tan a = 2)\\ \to B = \dfrac{2\dfrac{\sin a}{\cos a} - 3}{\dfrac{\sin a}{\cos a} + 1}\\ \to B = \dfrac{2\tan a - 3}{\tan a + 1}\\ \to B = \dfrac{2.2 - 3}{2 + 1} = \dfrac{1}{3}\\ 15) \, P = \dfrac{3\cos^2a + 2\sin^2a - 1}{\sin^2a - 3\cos^2a + 5} \qquad (\tan a = -3)\\ \to P = \dfrac{3 + 2\left(\dfrac{\sin a}{\cos a}\right)^2 - \dfrac{1}{\cos^2a}}{\left(\dfrac{\sin a}{\cos a}\right)^2 - 3 + \dfrac{5}{\cos^2a}}\\ \to P = \dfrac{3 + 2\tan^2a - (\tan^2a + 1)}{\tan^2a - 3 + 5(\tan^2a + 1)}\\ \to P = \dfrac{\tan^2a + 2}{6\tan^2a + 2}\\ \to P = \dfrac{(-3)^2 + 2}{6.(-3)^2 + 2} = \dfrac{11}{56}\end{array}$
