Find 
if 
tg = tan (tangent function)
Textbook solution is as lengthy as this:
But can I fast-path reasoning like
$tan(\alpha) = 1 => sin(\alpha) = cos(\alpha)$ (both sin and cos being either negative, or positive)
Now I just substitute $cos(\alpha) \ne0$ (because tan with such cos is defined) and just get $${7*cos(\alpha)-6*cos(\alpha)\over3*cos(\alpha)-5*cos(\alpha)} = \frac {cos(\alpha)}{-2*cos(\alpha)} = \frac {-1}{2}$$
Is my reasoning strict enough?