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What is the simplified value of \(\frac{{2{{\sin }^3}\theta - \sin \theta }}{{\cos \theta - 2{{\cos }^3}\theta }}?\)

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What is the simplified value of \(\frac{{2{{\sin }^3}\theta - \sin \theta }}{{\cos \theta - 2{{\cos }^3}\theta }}?\)


1). tan θ
2). sin θ
3). cos θ
4). cot θ


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Answered by on | Votes 0 |

(2sin3θ - sinθ)/(cosθ - 2cos3θ) = sinθ(2sin2θ - 1)/cosθ(1 - 2cos2θ)

Cos2θ = 2sin2θ - 1 = 1 - 2cos2θ

(2sin3θ - sinθ)/(cosθ - 2cos3θ) = sinθ/cosθ = tanθ

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