有一类三角函数取值范围问题,看似难以下手,但若能采用四则运算法则,对其 进行加、减、乘、除运算,将其转化为一个角的正(余)弦函数的形式,再运用正(余)弦 函数的有界性,则能获得十分简洁的解答. 例1 已知sinαcosβ=1/2,求t=cosαsinβ的取值范围. sinαcosβ+cosαsinβ=1/2+t, sin(α+β)=1/2+t, There is a range of trigonometric function values ​​that seem to be difficult to use, but if we can use a quadruple algorithm, add, subtract, multiply, and divide operations to convert it into the form of a positive (co) string function of an angle. By using the boundedness of the positive (co) chord function, a very concise solution can be obtained. Example 1 Given that sinαcosβ=1/2, find the value range of t=cosαsinβ. sinαcosβ+cosαsinβ=1/2+t, Sin(α+β)=1/2+t,