第1559题：重要不等式
在三角函数中，若 0<β<α<π20< \beta < \alpha < \dfrac{\pi}{2}0<β<α<2π ，则有( ).
A. α−β<sinα−sinβ\alpha - \beta <\sin \alpha - \sin \beta α−β<sinα−sinβ <tanα−tanβ< \tan \alpha -\tan \beta<tanα−tanβ
B. α+β<sinα+sinβ\alpha + \beta <\sin \alpha + \sin \beta α+β<sinα+sinβ<tanα+tanβ < \tan \alpha +\tan \beta<tanα+tanβ
C. sinα−sinβ<α−β\sin \alpha - \sin \beta <\alpha - \beta sinα−sinβ<α−β <tanα−tanβ<\tan \alpha -\tan \beta<tanα−tanβ
D. sinβ−sinα<β−α\sin \beta - \sin \alpha <\beta - \alpha sinβ−sinα<β−α <tanβ−tanα<\tan \beta -\tan \alpha<tanβ−tanα
