Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
2.9k views
in Trigonometry by (41.5k points)

If α, β, γ  are three real numbers and A = [(1, cos(α - β), cos(α - γ)), (cos(β - α), 1, cos(β - γ)), (cos(γ - α), cos(γ - β), 1)] then

(A) A is skew-symmetric

(B) A is invertible

(C) A is non-singular

(D) |A| = 0

1 Answer

+1 vote
by (41.3k points)
selected by
 
Best answer

Answer is (D) |A| = 0

Because cos(-θ) = cos θ ⇒ A is a symmetric matrix. 

Alternative solution: Given determinant can also be written as the product of two determinants as follows:

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...