# Exam-Style Question on Trigonometric Equations

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 596. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is not allowed.

(a) Show that $$2x+15+\dfrac{40}{x-3}= \dfrac{2x^2+9x-5}{x-3}, \quad x \in \mathbb{R}, x \neq 3$$

(b) Hence or otherwise, solve the equation $$2\cos{2\theta}+15+\dfrac{40}{\cos{2\theta}-3}=0, \quad \text{ for } 0 \le \theta \le \pi$$

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