## Exam-Style Questions on Trigonometric Identities## Problems on Trigonometric Identities adapted from questions set in previous Mathematics exams. |

## 1. | IB Analysis and Approaches |

(a) Show that:

$$ \cos 2x - \sin 2x + 1 = 2 \cos x ( \cos x - \sin x) $$(b) Hence or otherwise, solve the following equation for \( \pi \lt x \lt 3\pi \).

$$ \cos 2x - \sin 2x + 1 = \sin x - \cos x $$## 2. | IB Analysis and Approaches |

(a) Show that the equation \( 2 \sin^2 x - 5 \cos x = -1\) may be written in the form \( 2 \cos^2 x + 5 \cos x = 3\)

(b) Hence, solve the equation \( 2 \sin^2 x - 5 \cos x = -1 \), \( 2\pi \lt x \lt 4\pi \).

## 3. | 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 \(\sin 2A\).

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