# Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

IB Standard

Consider a right-angled triangle, ABC, with the right angle at vertex C and where $$\sin A = \frac{12}{13}$$

(a) Show that $$\cos A = \frac{5}{13}$$

(b) Find $$\sin 2A$$.

### 2.

A-Level

The cosine of acute angle $$\alpha$$ is $$\frac{1}{ \sqrt 5}$$

The angle $$\beta$$ is obtuse and $$\sin \beta = \sqrt \frac{2}{3}$$.

(a) Find exact values of $$\tan \alpha$$ and $$\tan \beta$$.

(b) Hence show that $$\tan( \alpha - \beta )$$ can be written as $$a+b \sqrt 2$$ where $$a$$ and $$b$$ are rational numbers

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