Mathematics

Problem

Solve the equation

\sin x = \tan x

and analyse the role of domain restrictions. a. (i) State precisely the set of real numbers for which the equation

\sin x = \tan x

is defined. b. (ii) Find all solutions of

\sin x = \tan x

in the interval

(-\pi,\pi)

, expressing each solution in simplest exact form. c. (iii) Derive the general solution of

\sin x = \tan x

for all permissible real values of

x

, clearly indicating any restrictions that arise from the domain of

\tan x