Mathematics

Mathematics

Problem

In △ABC\triangle ABC, right-angled at BB, let ∠A=θ\angle A=\theta. The side lengths are AB=8 cmAB=8\,\text{cm} and BC=6 cmBC=6\,\text{cm}. a. (i) Express tan⁡θ\tan\theta and sec⁡θ\sec\theta in terms of the given side lengths. b. (ii) Without using a calculator, verify that (1+tan⁡2θ)=sec⁡2θ(1+\tan^2\theta)=\sec^2\theta by substituting the expressions found in part (i). c. (iii) Hence, find the numerical value of sec⁡θ\sec\theta.

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