Find all solutions of the equation in the interval 0 2 pi If
Find all solutions of the equation in the interval [0, 2 pi). If there is no solution, enter No solution.) 9 sec x + 9 tan x = 9
Solution
9sec x + 9 tanx=9
sec x + tanx=1
(1/cosx) + (sinx/cosx)-1=0
1 + sinx - cos x=0
And - cos x + sin x= sqrt2 cos (pi/4 + x)
1 - sqrt2 cos(pi/4 + x)=0
sqrt cos(pi/4 + x)=1
cos (pi/4 + x)=1/sqrt2
pi/4 + x=pi/4 + 2pi n
x= 2pi n
In [0,2pi)
x= 0
