Which one of the following statements is an identity that holds true for all acute…

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

Problem

Which one of the following statements is an identity that holds true for all acute angles θ\theta? (a) sec⁡θ−cos⁡θ=tan⁡θ sin⁡θ\sec \theta-\cos \theta=\tan \theta\,\sin \theta (b) sec⁡θ−cos⁡θ=sin⁡θ\sec \theta-\cos \theta=\sin \theta (c) 1+tan⁡θ1+cot⁡θ=1\dfrac{1+\tan \theta}{1+\cot \theta}=1 (d) sec⁡2θ−tan⁡2θ=sin⁡2θ\sec^{2} \theta-\tan^{2} \theta=\sin^{2} \theta

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