sinx/cosx+cosx/sinx=4 怎么算啊

题目

sinx/cosx+cosx/sinx=4 怎么算啊

答案

sinx/cosx + cosx/sinx = 4
sin²x/(sinxcosx) + cos²x/(sinxcosx) = 4
(sin²x + cos²x)/(sinxcosx) = 4
1/(sinxcosx) = 4
sinxcosx = 1/4
sin2x = 1/2
2x = 2kπ + π/6 或2kπ + 5π/6
x = kπ + π/12 或 kπ + 5π/12 ,k ∈Z