Assertion (A) : For matrix A = [1 cos θ 1; – cos θ 1 cos θ; – 1 – cos θ 1], where θ ∈ [0, 2π], |A| ∈ [2, 4]. Reason (R) : cos θ ∈ [– 1, 1], ∀ θ ∈ [0, 2π].

Domain and Range of Trigonometric Functions, Determinant of a Matrix of Order Three | PadhAiPro

Question

Assertion-ReasonDomain and Range of Trigonometric FunctionsDeterminant of a Matrix of Order ThreeCBSE PYQ

If |–a b c; a –b c; a b –c| = kabc, then the value of k is :

Find the value of tan⁻¹(–1/√3) + cot⁻¹(1/√3) + tan⁻¹[sin(–π/2)].

Inverse Trigonometric Functions and Their Definitions

Principal Value Branch of Inverse Trigonometric Functions

Find the domain of the function f(x) = sin⁻¹(x² – 4). Also, find its range.

Solve the following system of equations, using matrices : 2/x + 3/y + 10/z = 4, 4/x – 6/y + 5/z = 1, 6/x + 9/y – 20/z = 2 where x, y, z ≠ 0

If A = [1 cot x; –cot x 1], show that A′A⁻¹ = [–cos 2x –sin 2x; sin 2x –cos 2x].

If |1 3 1; k 0 1; 0 0 1| = ± 6, then the value of k is :