4cos^2-1/tanα=0,求α

4cos^2-1/tanα=0,求α
4cos^2-1/tanα=0,求α

4cos^2-1/tanα=0,求α
4cos^2α--1/tanα=0
易知,tanα≠0,则
两边同乘tanα,得
4sinαcosα-1=0
2sin2α=1
sin2α=1/2
2α=π/6+2Kπ或5π/6+2Kπ(k∈z)
α=π/12+Kπ或5π/12+Kπ(k∈z)

首先a不= π/2+k π
4cosa^2-cosa/sina=0
则4cosa^2=cosa/sina
则cosa=0即a= π/2+k π
或4cosa=1/sina
则2sin2a=1,sin2a=1/2
则a=π/12+kπ或a=5π/12+kπ
所以a= π/2+k π或a=π/12+kπ或a=5π/12+kπ
综上a=π/12+kπ或a=5π/12+kπ