Sum and difference identities

Trigonometric sum and difference identities

Practise sine, cosine and tangent addition formulas through exact-angle calculations, symbolic expansions and geometric interpretation. This set connects familiar special angles with nonstandard angles and shows how signed ratios determine the result when two angles lie in specified quadrants.

Single-select and multiselect questions build from formula recognition to reconstructing missing ratios, recognizing a formula in reverse and checking whether a tangent expression is defined. Detailed solutions retain exact radicals, explain sign choices and identify errors such as adding sine values directly or using the wrong denominator sign.

Suggested approach

State the appropriate formula first, insert known values second, and simplify last. Sketch the relevant quadrants when recovering a missing cosine or sine. Calculator-free exact reasoning is sufficient unless a task explicitly says otherwise. This is focused practice for precalculus students who know unit-circle values and fundamental identities; it prepares you for double-angle formulas, phase representations and more involved trigonometric equations.