IB Maths AA HL Sl 3 6 Trigonometric Identities Questions

Practise using and deriving trigonometric identities, tracking restrictions, reducing equations to solvable forms and checking all valid branches.

Exam points

Apply sin²θ + cos²θ = 1 and related trigonometric ratios to simplify expressions or determine an unknown ratio without first finding the angle.
Use double-angle identities for sine and cosine to transform and solve trigonometric expressions, preserving the stated domain and signs.

[Maximum number: 2]

Show that $\frac{1-\cos 2 x}{2 \sin x} \equiv \sin x, x \neq k \pi$ where $k \in \mathbb{Z}$ .

$\frac{1-\cos 2 x}{2 \sin x} \equiv \frac{1-\left(1-2 \sin ^{2} x\right)}{2 \sin x}$ $\equiv \frac{2 \sin ^{2} x}{2 \sin x}$ $\equiv \sin x$
AG

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