Solution of the equation cosy=cosx
y = nπ + (−1)n x
y = 2nπ + x
nπ + x
cosy=cosx
cosx − cos y = 0
2sin (y+x)2.sin (y−x)2=0
sin (x+y)2 = 0 or sin (y−x)2 = 0
x+y2 = nπ or y−x2=nπ
x+y=2nπ or y−x=2nπ
or y=2nπ - x or y=2nπ+x
so,y=2nπ+x is the correct answer from options