(sinx+cosx)^2=1/2 поскореей плес

Question

(sinx+cosx)^2=1/2 поскореей плес

Answer 1

(sinx+cosx)^2=1/2

sin^2x+2sinxcosx+cos^2x=1/2

sin^2x+cos^2x+2sinxcosx=1/2

1+sin2x=1/2

sin2x=-1/2

2x=(-1)^(k+1)arcsin(1/2)+pi*k

2x=(-1)^(k+1)*pi/6+pi*k

x=(-1)^(k+1)*pi/12+pi*k/2