Factorising product of trig factors

A question is this type if and only if the equation is already in or can be directly factorised into a product of two trig factors (e.g. (tanθ+1)(sin²θ−3cos²θ)=0 or 6cosθtanθ−3cosθ+4tanθ−2=0) and each factor is solved separately.

2 questions · Standard +0.0

1.05o Trigonometric equations: solve in given intervals
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CAIE P1 2021 November Q3
4 marks Standard +0.3
3 Solve, by factorising, the equation $$6 \cos \theta \tan \theta - 3 \cos \theta + 4 \tan \theta - 2 = 0$$ for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).
AQA C2 2012 June Q7
7 marks Moderate -0.3
7 It is given that \(( \tan \theta + 1 ) \left( \sin ^ { 2 } \theta - 3 \cos ^ { 2 } \theta \right) = 0\).
  1. Find the possible values of \(\tan \theta\).
  2. Hence solve the equation \(( \tan \theta + 1 ) \left( \sin ^ { 2 } \theta - 3 \cos ^ { 2 } \theta \right) = 0\), giving all solutions for \(\theta\), in degrees, in the interval \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).