Mathematics

Mathematics

Problem

While proving the identity sec⁡2θ−1sec⁡θ=sin⁡θ\dfrac{\sec^{2}\theta-1}{\sec\theta}=\sin\theta, the left-hand side is first rewritten using a fundamental identity for sec⁡2θ\sec^{2}\theta. What is the resulting expression after this single substitution? a) tan⁡θsec⁡θ\dfrac{\tan\theta}{\sec\theta} b) tan⁡2θ sec⁡θ\tan^{2}\theta\,\sec\theta c) tan⁡2θsec⁡θ\dfrac{\tan^{2}\theta}{\sec\theta} d) tan⁡2θcos⁡θ\dfrac{\tan^{2}\theta}{\cos\theta}

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