Number of solutions of the equationtan x + sec x = 2 cos x, lying in the interval [0, 2p] is

tan x + sec x = 2 cos x
sin x + 1 = 2 cos²x
sin x + 1 = 2 (1 - sin²x)
2 sin²x + sin x - 1 = 0
Solve for sin x:
sin x = - 1, or sin x = 1/2
sin x = -1 means cos x = 0, which is not possible as tan x cant be infinity
Therfore, sin x = 1/2
x = p or x = p - (p / 6), in the interval [0, 2p]
x = p or x = 5p / 6 are the two solutions
Thanks

2 solutions pi/6 5pi/6