- In this question you must show detailed reasoning.
Solutions relying entirely on calculator technology are not acceptable.
- Show that the equation
$$4 \tan x = 5 \cos x$$
can be written as
$$5 \sin ^ { 2 } x + 4 \sin x - 5 = 0$$
- Hence solve, for \(0 < x \leqslant 360 ^ { \circ }\)
$$4 \tan x = 5 \cos x$$
giving your answers to one decimal place.
- Hence find the number of solutions of the equation
$$4 \tan 3 x = 5 \cos 3 x$$
in the interval \(0 < x \leqslant 1800 ^ { \circ }\), explaining briefly the reason for your answer.