Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Matrices

NDA 2017 · Mathematics · Matrices

If A=[ array ll θ & θ - θ & θ array ] , then what is A^3 equal to?

If A=\left[cos⁡θsin⁡θ−sin⁡θcos⁡θ\begin{array}{ll}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right], then what is A3A^3 equal to?

Options

  1. A\left[cos⁡3θsin⁡3θ−sin⁡3θcos⁡3θ\begin{array}{ll}\cos 3 \theta & \sin 3 \theta \\ -\sin 3 \theta & \cos 3 \theta\end{array}\right]
  2. B\left[cos⁡3θsin⁡3θ−sin⁡3θcos⁡3θ\begin{array}{cc}\cos ^3 \theta & \sin ^3 \theta \\ -\sin ^3 \theta & \cos ^3 \theta\end{array}\right]
  3. C\left[cos⁡3θ−sin⁡3θsin⁡3θcos⁡3θ\begin{array}{cc}\cos 3 \theta & -\sin 3 \theta \\ \sin 3 \theta & \cos 3 \theta\end{array}\right]
  4. D\left[cos⁡3θ−sin⁡3θsin⁡3θcos⁡3θ\begin{array}{cc}\cos ^3 \theta & -\sin ^3 \theta \\ \sin ^3 \theta & \cos ^3 \theta\end{array}\right]

Correct answer

A. \left[cos⁡3θsin⁡3θ−sin⁡3θcos⁡3θ\begin{array}{ll}\cos 3 \theta & \sin 3 \theta \\ -\sin 3 \theta & \cos 3 \theta\end{array}\right]

Step-by-step solution

A=\left[cos⁡θsin⁡θ−sin⁡θcos⁡θ\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right] We know, A^n=\left[cos⁡nθsin⁡nθ−sin⁡nθcos⁡nθ\begin{array}{cc}\cos n \theta & \sin n \theta \\ -\sin n \theta & \cos n \theta\end{array}\right]\therefore A^3=\left[cos⁡3θsin⁡3θ−sin⁡3θcos⁡3θ\begin{array}{cc} \cos 3 \theta & \sin 3 \theta \\ -\sin 3 \theta & \cos 3 \theta \end{array}\right]
Practice Matrices on Quantrex Academy →

More from Matrices

Consider the following statements : I. If n× n(n > 1) matrix is symmetric, then its… NDA 2026If M is a square matrix such that M^3=M , then how many values of |M| are possible ? NDA 2026If M_k= bmatrix k & k-1 k-1 & k bmatrix where k is a natural number, then what is… NDA 2026If M^ T is the transpose of a 2×2 matrix M , then which of the following is/are correct ?… NDA 2026Consider the following in respect of non-singular matrices A and B : I. (AB)^ -1 = A^ -1… NDA 2025For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is [adj\… NDA 2025Consider the following statements about the matrix M = pmatrix 71 & 23 & 48 57 & 28 & 29… NDA 2025If [x \ 1 \ 1] pmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 pmatrix pmatrix 1 1 x pmatrix = [45]… NDA 2025If A = pmatrix 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 pmatrix , then what is A^2 - 4A equal to? NDA 2025If A = pmatrix y & z & x z & x & y x & y & z pmatrix where x , y , z are integers, is an… NDA 2025If A = pmatrix x & y & z y & z & x z & x & y pmatrix where x , y , z are integers, is an… NDA 2025For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is the… NDA 2025What is the value of the determinant of the inverse of the matrix pmatrix -4 & -5 2 & 2… NDA 2025If f(θ) = pmatrix θ & θ - θ & θ pmatrix , then what is \ f(π)\ ^2 equal to? NDA 2025Let X be a matrix of order 3 × 3, Y be a matrix of order 2 × 3 and Z be a matrix of order… NDA 2024Let A and B be two square matrices of same order. If A B is a null matrix, then which one… NDA 2024 Full Matrices list Matrices JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs