Solve equation with tan2x or mixed tan/double angle

Solve a trigonometric equation containing tan2x, or a product/ratio of tan and double angle terms (e.g. tan x tan 2x = 1, tan 2x = 5 cot x), typically by expanding tan2x and simplifying.

4 questions · Standard +0.3

1.05o Trigonometric equations: solve in given intervals
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CAIE P2 2014 June Q2
4 marks Standard +0.3
2 Solve the equation \(3 \sin 2 \theta \tan \theta = 2\) for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).
CAIE P3 2013 June Q3
5 marks Standard +0.3
3 Solve the equation \(\tan 2 x = 5 \cot x\), for \(0 ^ { \circ } < x < 180 ^ { \circ }\).
CAIE P3 2019 June Q3
5 marks Standard +0.3
3 Showing all necessary working, solve the equation \(\cot 2 \theta = 2 \tan \theta\) for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).
CAIE P3 2006 November Q2
4 marks Standard +0.3
2 Solve the equation $$\tan x \tan 2 x = 1 ,$$ giving all solutions in the interval \(0 ^ { \circ } < x < 180 ^ { \circ }\).