Mathematics

Mathematics

Problem

In a right-angled triangle ABCABC, right-angled at CC, let ∠A=θ\angle A=\theta and ∠B=90∘−θ\angle B=90^{\circ}-\theta. a. (i) If sin⁡θ=513\sin\theta=\dfrac{5}{13}, find cos⁡(90∘−θ)\cos(90^{\circ}-\theta). b. (ii) Using the result of part (i), determine sec⁡(90∘−θ)\sec(90^{\circ}-\theta). c. (iii) Hence, calculate the value of sin⁡θ+cos⁡(90∘−θ)tan⁡(90∘−θ)\dfrac{\sin\theta+\cos(90^{\circ}-\theta)}{\tan(90^{\circ}-\theta)}.

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