sin2x+2cos^2X=0 sin2x+1=0 sin4x-sin7x=0

Question

sin2x+2cos^2X=0

sin2x+1=0

sin4x-sin7x=0

Answer 1

sin2x+2cos^2X=0

2sinxcosx+2cos^2x=0

2cosx(sinx+cosx)=0

x=П/2(2k+1)

sinx+cosx=0

tgx=-1

x=-П/4+Пk

sin2x+1=0  sin2x=-1  2x=-П/2+2Пk    x=-П/4+Пk

sin4x-sin7x=0 -2sin3x/2cos11x/2=0 

sin3x/2=0  3x/2=Пk  x=2Пk/3

cos11x/2=0

11x/2=П/2(2k+1)

x=П/11(2k+1)