Mathematics

Mathematics

Problem

A student is verifying the identity (sec⁡θ−tan⁡θ)(sec⁡θ+tan⁡θ)=1(\sec\theta-\tan\theta)(\sec\theta+\tan\theta)=1. After expanding, the student obtains sec⁡2θ−tan⁡2θ\sec^2\theta-\tan^2\theta. Which of the following identities will correctly complete the proof? a) tan⁡2θ=sec⁡2θ+1\tan^2\theta=\sec^2\theta+1 b) 1+tan⁡2θ=sec⁡2θ1+\tan^2\theta=\sec^2\theta c) sec⁡2θ+tan⁡2θ=1\sec^2\theta+\tan^2\theta=1 d) sin⁡2θ+cos⁡2θ=1\sin^2\theta+\cos^2\theta=1

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