Question

2sin²(x-\(\frac{\pi}{4}\)) =2\(\sin^2x-\tan x\)

 

 

Answer 1

tham khảo

Đk: cosx # 0 ↔ x # pi/2+ kpi 

[ căn 2sin(x-pi/4)]^2 - 2sin^2x+ sinx/ cosx = 0 

↔ (sinx - cosx)^2 . cosx - 2sin^2x. cosx + sinx = 0 

↔ (1- sin2x ).cosx - 2sin^2x. cosx + sinx = 0 

↔ cosx - 2sinx.cos^2x- 2sin^2x. cosx + sinx = 0 

↔(cosx+ sinx) - 2sinx.cosx(cosx+sinx)= 0 

↔(cosx+sinx) ( 1- sin2x ) = 0 

↔ [cosx+sinx = 0 
....[ 1- sin2x = 0 

↔ [căn2cos(x- pi/4) = 0 
....[ sin2x = 1 

↔ [x= 3pi/4 + kpi ( k thuộc Z); tm 
....[ x= pi/4 + kpi ( k thuôc Z) ; tm