Выполните вычисления (3sin^2a+12sina*cosa+cos^a)/(sin^2a+sina*cosa-2cos^2a); если tga=2.

\[\frac{3\sin^{2}a + 12\sin a\cos a + \cos^{2}a}{\sin^{2}a + \sin a\cos a - 2\cos^{2}a};\]

\[если\ tg\ a = 2:\]

\[\frac{3 \cdot \frac{\sin^{2}a}{\cos^{2}a} + 12 \cdot \frac{\sin a\cos a}{\cos^{2}a} + \frac{\cos^{2}a}{\cos^{2}a}}{\frac{\sin^{2}a}{\cos^{2}a} + \frac{\sin a\cos a}{\cos^{2}a} - 2 \cdot \frac{\cos^{2}a}{\cos^{2}a}} =\]

\[= \frac{3tg^{2}a + 12\text{tg}a \cdot 1 + 1}{tg^{2}a + tga \cdot 1 - 2 \cdot 1} =\]

\[= \frac{3 \cdot 2^{2} + 12 \cdot 2 + 1}{2^{2} + 2 - 2} =\]

\[= \frac{12 + 24 + 1}{4} = \frac{37}{4} = 9\frac{1}{4}.\]