- (a) Given that \(t = \tan \frac { X } { 2 }\) prove that
$$\cos x \equiv \frac { 1 - t ^ { 2 } } { 1 + t ^ { 2 } }$$
(b) Show that the equation
$$3 \tan x - 10 \cos x = 10$$
can be written in the form
$$( t + 2 ) \left( a t ^ { 2 } + b t + c \right) = 0$$
where \(t = \tan \frac { X } { 2 }\) and \(a , b\) and \(c\) are integers to be determined.
(c) Hence solve, for \(- 180 ^ { \circ } < x < 180 ^ { \circ }\), the equation
$$3 \tan x - 10 \cos x = 10$$