Technique

Determinants with trigonometric entries

\sin^2\theta + \cos^2\theta = 1

$\theta$: the angle appearing in the entries

Determinants whose entries are trigonometric functions almost always collapse through a Pythagorean or compound-angle identity rather than through brute expansion.

questions use it

of them past-year

2017–2026

years it has appeared

26%

rated HARD

exams

Matrices & Determinants notes Open all 47 in the paper builder

Used alongside

How often each of these appears in the same solution as this one.

Cofactor expansion11
Rules of transposition9
Row and column operations8
Proportional rows make a determinant vanish6
Determinant of a 2×2 matrix5
Orthogonal matrices5

47 questions whose solution uses this

Every one was read individually — a question is here because its solution invokes this, not because the stem mentions it.

Every identity this chapter tests, with its own question set.

All Matrices & Determinants formulas