Mathematics

Mathematics

Problem

For an acute angle θ\theta, it is given that sin⁡θ−cos⁡θ=13\sin\theta - \cos\theta = \dfrac{1}{3}. Solve the following. a. (i) Show that sin⁡θ+cos⁡θ=173\sin\theta + \cos\theta = \dfrac{\sqrt{17}}{3}. b. (ii) Hence find tan⁡θ\tan\theta. c. (iii) Further evaluate (sec⁡θ−tan⁡θ)(\sec\theta - \tan\theta) and leave your answer in simplest radical form.

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