Which of the following statements are always correct

MATHEMATICS · Multi correct · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Which of the following statements are always correct, where Q\mathbb{Q} denotes the set of rational numbers? (1) cos⁡2θ∈Q\cos2\theta\in\mathbb{Q} and sin⁡2θ∈Q⇒tan⁡θ∈Q\sin2\theta\in\mathbb{Q}\Rightarrow\tan\theta\in\mathbb{Q}, if defined (2) tan⁡θ∈Q⇒sin⁡2θ\tan\theta\in\mathbb{Q}\Rightarrow\sin2\theta, cos⁡2θ\cos2\theta, and tan⁡2θ∈Q\tan2\theta\in\mathbb{Q}, if defined (3) If sin⁡θ∈Q\sin\theta\in\mathbb{Q} and cos⁡θ∈Q\cos\theta\in\mathbb{Q}, then tan⁡3θ∈Q\tan3\theta\in\mathbb{Q}, if defined (4) If sin⁡θ∈Q\sin\theta\in\mathbb{Q}, then cos⁡3θ∈Q\cos3\theta\in\mathbb{Q}

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