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

Use sinÂ²Î¸+cosÂ²Î¸=1 and ratio relationships to find a missing trig value or eliminate an angle from an expression.
Apply and derive double-angle or half-angle identities to rewrite powers, products or exact-angle expressions in the required form.
Manipulate a trigonometric identity line by line, tracking non-zero denominators and stated angle restrictions.
Use identities to reduce a trigonometric equation or a geometric/model expression to a solvable algebraic form, then check the valid branches.

[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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