## 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 numbersIf you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.

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