Challenging +1.8 This AEA question requires non-routine algebraic manipulation to transform tan x into a double angle form, demanding insight to multiply by cos x, apply sin 2x = 2sin x cos x, and recognize √3 relates to 60°. Part (b) then requires solving the resulting equation. The transformation isn't standard textbook fare and requires multiple sophisticated steps with trigonometric identities.
2.(a)Show that the equation
$$\tan x = \frac { \sqrt { 3 } } { 1 + 4 \cos x }$$
can be written in the form
$$\sin 2 x = \sin \left( 60 ^ { \circ } - x \right)$$
(b)Solve,for \(0 < x < 180 ^ { \circ }\)
$$\tan x = \frac { \sqrt { 3 } } { 1 + 4 \cos x }$$
2.(a)Show that the equation
$$\tan x = \frac { \sqrt { 3 } } { 1 + 4 \cos x }$$
can be written in the form
$$\sin 2 x = \sin \left( 60 ^ { \circ } - x \right)$$
(b)Solve,for $0 < x < 180 ^ { \circ }$
$$\tan x = \frac { \sqrt { 3 } } { 1 + 4 \cos x }$$
\hfill \mbox{\textit{Edexcel AEA 2017 Q2 [9]}}