Mathematics

Mathematics

Problem

Triangle ABCABC is right-angled at CC with AC=8 cmAC = 8\,\text{cm} and BC=15 cmBC = 15\,\text{cm}. Let ∠A=θ\angle A = \theta. a. (i) Find sin⁡θ\sin \theta and cos⁡θ\cos \theta in simplest form. b. (ii) Hence calculate (sin⁡θ+cos⁡θ)2(\sin \theta + \cos \theta)^{2}, simplifying your result. c. (iii) Show that (sin⁡θ+cos⁡θ)2+(sin⁡θ−cos⁡θ)2=2(\sin \theta + \cos \theta)^{2} + (\sin \theta - \cos \theta)^{2} = 2. Provide full working to justify each step.

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