PYQ - Prove the following — task. Maths CBSE Live product, Class 10 (2026-27).

Derive that \(\dfrac{\sin \theta - 2\sin^3 \theta}{\cos \theta - 2\cos^3 \theta} + \tan \theta = 0\).

Proof:

\(\dfrac{\sin \theta - 2\sin^3 \theta}{\cos \theta - 2\cos^3 \theta}+ \tan \theta\)

= \frac{\sin θ (i - {2 i}^{i} θ)}{\cos θ (i - {2 i}^{i} θ)} + \tan θ

= \frac{\sin θ (1 - 2 i^{2} θ)}{\cos θ (1 - 2 (i - i^{2} θ))} + \tan θ

= \frac{i θ (1 - 2 i^{2} θ)}{- i + 2 i^{2} θ} + \tan θ

= - i θ + \tan θ

= i

Hence proved.

[Note: Enter minus symbol wherever necessary]

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5. PYQ - Prove the following