题目

已知,sin（π/4 2α）*sin（π/4-2α）,α∈（π/4,π/2）求2sin²α tanα-1/tanα-1

提问时间：2021-01-05

答案

题目应该是已知sin(π/4+2α）·sin(π/4-2α)=1/4,α∈（π/4,π/2),求2sin^2α+tanα-1/tanα-1的值
sin(π/4+2α)sin(π/4-2α)
=1/2*(cos(π/4+2α-π/4+2α)-cos(π/4+2α+π/4-2α))
=1/2*(cos(4α)-cos(π/2))
=1/2*cos(4α)
=1/4
所以cos(4α)=1/2
因为α属于(π/4,π/2)
所以π