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.

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.

Filter

Showing 47 of 47 questions — easiest first, then oldest paper first.

#1NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#2NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#3NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#4NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#5NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#6NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations
Strategy Concept notes
#7NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#8NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#9CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#10CBSE Class 12 → Mathematics → Matrices → Transpose of a Matrix
#11NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#12NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#13CBSE Class 12 → Mathematics → Matrices → Transpose of a Matrix
#14NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#15NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#16NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#17NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#18NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#19NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#20NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#21NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#22NDA → Mathematics → Matrices & Determinants → Cofactors, Adjoint, and Inverse
Strategy Concept notes
#23NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#24NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
Set · 1 question
Consider the following for the next three (03) items that follow: Let $A = \begin{pmatrix} 0 & \sin^2\theta & \cos^2\theta \\ \cos^2\theta & 0 & \sin^2\theta \\ \sin^2\theta & \cos^2\theta & 0 \end{pmatrix}$ and $A = P + Q$ where P is symmetric matrix and Q is skew-symmetric matrix.
- #25NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
  Strategy Concept notes
#26CBSE Class 12 → Mathematics → Matrices → Transpose of a Matrix
#27CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
#28NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#29CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices
#30NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#31MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities
Strategy Concept notes
#32CBSE Class 12 → Mathematics → Matrices → Transpose of a Matrix
#33NDA → Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
Strategy Concept notes
#34CBSE Class 12 → Mathematics → Matrices → Transpose of a Matrix
#35CBSE Class 12 → Mathematics → Matrices → Transpose of a Matrix
#36NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#37NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#38NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#39NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#40NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#41Maharashtra HSC Class 12 → Mathematics → Matrices → Inverse by Adjoint Method
#42CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#43NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
Strategy Concept notes
#44NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#45NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
Strategy Concept notes
#46MHT-CET → Maths → Determinants and Matrices → Determinants, Cofactors and the Adjoint Identities
Strategy Concept notes
#47MHT-CET → Maths → Determinants and Matrices → Inverse of a Matrix — Adjoint Formula, Products and Verification
Strategy Concept notes

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

All Matrices & Determinants formulas