若f（x）=2tanx-2sin2x2−1sinx2cosx2，则f(π12)的值为．

Question

若f（x）=2tanx-(2sin2(x)/(2)−1)/(sin(x)/(2)cos(x)/(2))，则f((π)/(12))的值为______．

Answer 1

∵f（x）=2tanx-(2sin2(x)/(2)−1)/(sin(x)/(2)cos(x)/(2))=2 ((sinx)/(cosx)+(cosx)/(sinx))=(2)/(sinxcosx)＝(4)/(sin2x)
∴f((π)/(12)) ＝(4)/(sin(π)/(6))＝8
故答案为：8