COMEDK · Maths · 8. Trigonometric Ratios & Identities
The expression \(\frac{\sin \theta-2 \sin ^3 \theta}{2 \cos ^3 \theta-\cos \theta}\) is equal to
- A \(\cot \theta\)
- B \(\tan \theta\)
- C \(\sec \theta \tan \theta\)
- D \(\tan \theta \sin \theta\)
Answer & Solution
Correct Answer
(B) \(\tan \theta\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } t=\frac{\sin \theta-2 \sin ^3 \theta}{2 \cos ^3 \theta-\cos \theta} \\ & t=\frac{\sin \theta\left[1-2 \sin ^2 \theta\right]}{\cos \theta\left[2 \cos ^2 \theta-1\right]} \quad\left[\because \tan \theta=\frac{\sin \theta}{\cos \theta}\right] \\ &…
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