Show that the equation
$$4 \tan \theta \sin \theta = 15$$
can be written as
$$4 \sin ^ { 2 } \theta = 15 \cos \theta$$
(1 mark)
Use an appropriate identity to show that the equation
$$4 \sin ^ { 2 } \theta = 15 \cos \theta$$
can be written as
$$4 \cos ^ { 2 } \theta + 15 \cos \theta - 4 = 0$$
Solve the equation \(4 c ^ { 2 } + 15 c - 4 = 0\).
Hence explain why the only value of \(\cos \theta\) which satisfies the equation
$$4 \cos ^ { 2 } \theta + 15 \cos \theta - 4 = 0$$
is \(\cos \theta = \frac { 1 } { 4 }\).
Hence solve the equation \(4 \tan \theta \sin \theta = 15\) giving all solutions to the nearest \(0.1 ^ { \circ }\) in the interval \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).
Write down all the values of \(x\) in the interval \(0 ^ { \circ } \leqslant x \leqslant 90 ^ { \circ }\) for which
$$4 \tan 4 x \sin 4 x = 15$$
giving your answers to the nearest degree.