Explanation:

secx + tanx = √3

1/cosx  +sinx/cosx  =√3

1+  sinx  =√3  cosx

Dividing by 2

√3/2  cosx –1/2sinx =1/2

Cosπ/6  cosx  -sinπ/6  sinx =1/2

Cos(x +π/6) =1/2

0≤x≤3π

π/6 ≤ x+π/6 ≤3π +π/6

x=π/6 ,3π/2  ,13π/6

at x=3π/2  tanx and sec x not valid

number of solution  2