 # 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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