1998年成人高考文科数学试题的第(21)题:如果 sinα+cosα=1/5(0<α<π)那么 tanα的值是____。这是一道利用三角函数恒等变换的“给式求值”的填空题,解答此题时需要利用同角三角函数的基本关系式,两角和与两角差的三角公式,倍角公式,半角公式,万能公式,甚至诱导公式,和差化积公式等,使用公 In the adult mathematics test of the 1998 adult mathematics question (21), if sinα+cosα=1/5 (0<α<π) then the value of tanα is ____. This is a fill-in question of “giving value evaluation” using the trigonometric function identity transformation. When solving this question, it is necessary to use the basic relational expression of the same-angle trigonometric function, the triangle formula of the two angles and the difference between the two angles, the double-angle formula, and the half-angle. Formulas, universal formulas, even induction formulas, and differential product formulas, etc.