Problem

Problem

Which of the following statements are always correct? (where, QQ denotes the set of rationals) a. cos⁡2θ∈Q\cos 2\theta \in Q and sin⁡2θ∈Q⇒tan⁡θ∈Q\sin 2\theta \in Q \Rightarrow \tan \theta \in Q (if defined) b. tan⁡θ∈Q⇒sin⁡2θ,cos⁡2θ\tan \theta \in Q \Rightarrow \sin 2\theta, \cos 2\theta and tan⁡2θ∈Q\tan 2\theta \in Q (if defined) c. If sin⁡θ∈Q\sin \theta \in Q and cos⁡θ∈Q⇒tan⁡3θ∈Q\cos \theta \in Q \Rightarrow \tan 3\theta \in Q (if defined) d. If $\sin \theta \in Q \Rightarrow \cos 3\theta \in Q

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