cos(α-π/2)*tan(-α-3π/2)*sec(-α+5π/2)*tan(α+5π/2)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 23:35:15
cos(α-π/2)*tan(-α-3π/2)*sec(-α+5π/2)*tan(α+5π/2)cos(α-π/2)*tan(-α-3π/2)*sec(-α+5π/2)*tan(α+5π/2)cos(

cos(α-π/2)*tan(-α-3π/2)*sec(-α+5π/2)*tan(α+5π/2)
cos(α-π/2)*tan(-α-3π/2)*sec(-α+5π/2)*tan(α+5π/2)

cos(α-π/2)*tan(-α-3π/2)*sec(-α+5π/2)*tan(α+5π/2)
由于余弦函数是偶函数,∴ cos(α-π/2) = cos(π/2-α)
cos(α-π/2)*tan(-α-3π/2)*sec(-α+5π/2)*tan(α+5π/2)
= cos(π/2-α) * tan(2π-α-3π/2) * sec(-α+5π/2-2π) *tan(α+5π/2 -2π)
=cos(π/2-α) * tan(π/2 - α ) * sec(π/2 -α) * tan( π/2+α)
= sinα ﹡cotα ﹡ cscα﹡(-cotα)
= - (sinα ﹡cscα) cot²α
= - cot²α