化简(2cosα-1)/(2tan(π/4-α)*sin(π/4+α))

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/20 03:50:04
化简(2cosα-1)/(2tan(π/4-α)*sin(π/4+α))化简(2cosα-1)/(2tan(π/4-α)*sin(π/4+α))化简(2cosα-1)/(2tan(π/4-α)*sin

化简(2cosα-1)/(2tan(π/4-α)*sin(π/4+α))
化简(2cosα-1)/(2tan(π/4-α)*sin(π/4+α))

化简(2cosα-1)/(2tan(π/4-α)*sin(π/4+α))
2tan(π/4-α)*sin(π/4+α)
= 2sin(π/4-α)*sin(π/4+α)/[cos(π/4 - α)]
而2sin(π/4-α)*sin(π/4+α)
= 2cos[(π/2) - (π/4-α)]·cos[(π/2) - (π/4+α)]
= 2cos[(π/4)+α]·cos[(π/4)-α]
∴原式 = (2cosα - 1)/2cos[(π/4)+α]