The correct option is C 7
Given equation iscosx+cos2x+cos3x+cos4x=0⇒(cosx+cos3x)+(cos2x+cos4x)=0⇒2cos2xcosx+2cos3xcosx=0⇒2cosx(cos2x+cos3x)=0⇒2cosx(2cos5x2cosx2)=0⇒cosx⋅cos5x2⋅cosx2=0⇒cosx=0or cos5x2=0or cosx2=0Now, cosx=0⇒x=π2, 3π2 [∵0≤x<2π]cos5x2=0⇒5x2=π2, 3π2, 5π2, 7π2, 9π2, 11π2,....⇒x=π5, 3π5, π, 7π5, 9π5 [∵0≤x<2π]and cosx2=0⇒x2=π2, 3π2, 5π2,......⇒x=π [∵0≤x<2π]Hence, x=π2, 3π2, π, π5, 3π5, 7π5, 9π5