sin(3π+α )=1/4,求cos(π+α)/cosα[cos(π+α)-1]+cos(α-2π)/cos(α+2π)cos(π+α)+coa(-α)

题目

sin(3π+α )=1/4,求cos(π+α)/cosα[cos(π+α)-1]+cos(α-2π)/cos(α+2π)cos(π+α)+coa(-α)

答案

解 sin(3π+α )=1/4 sin α =-1/4 cos α=±√15/4
cos(π+α)/cosα[cos(π+α)-1]+cos(α-2π)/cos(α+2π)cos(π+α)+cos(-α)
=-cosα/cosα[-cos α -1]+cosα/cosα（-cosα)+cos α
=cosα/cosα[ cos α +1]+（-cosα)+coa α
=[ cos α +1]+2cos α
=3coa α+1=±√15/4+1