Given that $$$\cos \left(x-30^{\circ}\right)=2 \sin \left(x+30^{\circ}\right)$$$, show that $$$\tan x=\frac{2-\sqrt{3}}{1-2 \sqrt{3}}$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_31 Year：2021 Question No：3(a)

Answer:

Use correct trig expansions and obtain an equation in $\sin x$ and $\cos x$
Use correct exact trig ratios for $30^{\circ}$ in their expansion
Obtain an equation in $\tan x$
Obtain $\tan x=\frac{2-\sqrt{3}}{1-2 \sqrt{3}}$ from correct working

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