2sinx*cosx+√2cosx-√2sinx-1=0

Question

2sinx*cosx+√2cosx-√2sinx-1=0

Answer 1

-(COSX-SINX)^2+SQRT(2)(COSX-SINX)=0

(COSX-SINX)(SQRT(2)-COSX+SINX)=0

COSX=SINX

TGX=1

x=П/4+Пk

cosx-sinx=sqrt(2)

(sqrt(2)/2)cosx-(sqrt(2)/2)sinx=1

cos(П/4+x)=1

x=2пk-п/4

Answer 2

2sinx*cosx+√2cosx-√2sinx-1=0

√2cosx(√2sinx+1)-1(√sinx+1)=0

(√2sinx+1)(√2cosx-1)=0

sinx=-√2/2  x=-П/4+Пн

cosx=√2/2    x=П/4+2Пн