Find all solutions on the interval [0,2pi). (Answer as a comma-separated list. Round answer to four decimal places)

Question

cos(5x)cos(4x) + sin(5x)sin(4x) =1

Answer 1

= cos(5x-4x)= cos(x)= 1

x = cos^-1(1)= exactly 0

check the answer

cos(0)cos(0)+sin(0)sin(0)= 1(1)+0(0)= 1

x= 0 or 0.0000..., but no rounding as an approximation since it's exactly zero

and it's the only solution in the given interval

x would = 2npi with n= any integer, but only n=0 is within the interval [0,2pi)

had the interval been [0,2pi] then x=0, 2pi, with two solutions

] includes the end point, ) excludes the end point

use the formula cos(a-b)= cosacosb +sinasinb with a=5x, b=4x