Question

sin(x+п/6)+cos(x+п/3)=1+cos2x

Answer 1

√3/2sinx+1/2cosx+1/2cosx-√3/2sinx=cosx

1+cos2x=sin^2x+cos^2x+cos^2x-sin^2x=2cos^2x

cosx=2cos^2x

2cos^2x-cosx=0

cosx=0

x=П/2+Пk

cosx=1/2

x=+-П/3+2Пk