Question

how do i solve tan3x+1 = sec3x

Answer 1

on the interval 0,2pie

Answer 2

you could try converting this to sines and cosines
sin 3x 1
----- + 1 = ------
cos 3x cos 3x

sin 3x + cos 3x = 1

now solve this by complementary angle method

there might be an easier way to do this ....

Answer 3

by inspection one root is x = 0
as tan 0 = 0 and sec 0 = 1

Answer 4

also 3x = 2pi (as tan 2pi = 0 and sec 2pi = 1)

so x = 2pi/3 is a root

and 3x = 4pi so another root = 4pi/3

so in the interval (0,2pi) the solutions are

2pi/3 and 4pi/3

Answer 5

i've not included x = 0 because i've assumed its an open interval ( not including 0 and 2pi)- if its includes these then another 2 roots are 0 and 2pi