\(\frac{\text{(sinθ - 2sin³θ)}}{\text{(2cos³θ - cosθ)}} = \text{tan θ}\)
L.H.S =\(\frac{\text{(sinθ - 2sin³θ)}}{\text{(2cos³θ - cosθ)}}\)
Simplifying the L.H.S:
\(\frac{\text{sinθ (1 - 2sin²θ)}}{\text{cosθ {2(1 - sin²θ) - 1}}}\)
\(= \frac{\text{sinθ (1 - 2sin²θ)}}{\text{cosθ(2 - 2sin²θ - 1)}}\)
\(=\frac{\text{ sinθ (1 - 2sin²θ)}}{\text{cosθ(1 - 2sin²θ)}}\)
\(=\frac{ \text{sinθ}}{\text{cosθ}}\)
\(=\text{ tanθ}\)
= R.H.S