3sin^2x-7sinxcosx+6cos^2x=1

来源：百度知道编辑：UC知道时间：2024/06/05 05:08:04

3sin^2x-7sinxcosx+6cos^2x=1
(sin^2x+cos^2x)+2sin^2x-7sinxcosx+5cos^2x=1
1+2sin^2x-7sinxcosx+5cos^2x=1
2sin^2x-7sinxcosx+5cos^2x=0
(2sinx-5cosx)(sinx-cosx)=0
2sinx=5cosx,sinx=cosx
tanx=sinx/cosx=5/2或=1
x=kπarctan5/2或x=kπ+π/4
k是整数

3sin^2x-7sinxcosx+6cos^2x=1
2sin^2x-7sinxcosx+5cos^2x=0
(2sinx-5cosx)(sinx-cosx)=0
sinx=2.5cosx
(cosx)^2=4/29
cosx=2sqrt(29)/29或cosx=-2sqrt(29)/29
sinx=5sqrt(29)/29或sinx=-5sqrt(29)/29
x=asin(5sqrt(29)/29)+k*pi，k为整数
或sinx=cosx
x=pi/4+k*pi，k为整数

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