If and , where , are the roots of , then…

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If x=nπ+(−1)nαx=n\pi+(-1)^n\alpha and x=nπ+(−1)nβx=n\pi+(-1)^n\beta, where n∈Zn\in\mathbb{Z}, are the roots of 4cos⁡x−3sec⁡x=tan⁡x4\cos x-3\sec x=\tan x, then 4(sin⁡α+sin⁡β)4(\sin\alpha+\sin\beta) is (1) −1-1 (2) 11 (3) 22 (4) None of these

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