Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` is ______.

The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.

The value of the expression (cos^–1x)² is equal to sec²x.

The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.

The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.

The minimum value of n for which `tan^-1  "n"/pi > pi/4`, n ∈ N, is valid is 5.

The principal value of `sin^-1 [cos(sin^-1  1/2)]` is `pi/3`.

Addition of matrices is defined if order of the matrices is ______.

If possible, find the sum of the matrices A and B, where A = `[(sqrt(3), 1),(2, 3)]`, and B = `[(x, y, z),(a, "b", 6)]`

If A = `[(1, 2),(-2, 1)]`, B = `[(2, 3),(3, -4)]` and C = `[(1, 0),(-1, 0)]`, verify: A(B + C) = AB + AC

If A = `[(2, 1)]`, B = `[(5, 3, 4),(8, 7, 6)]` and C = `[(-1, 2, 1),(1, 0, 2)]`, verify that A(B + C) = (AB + AC).

If A = `[(1, 0, -1),(2, 1, 3 ),(0, 1, 1)]`, then verify that A² + A = A(A + I), where I is 3 × 3 unit matrix.

If A = `[(1, 2),(4, 1),(5, 6)]` B = `[(1, 2),(6, 4),(7, 3)]`, then verify that: (2A + B)′ = 2A′ + B′

Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A + (B + C) = (A + B) + C

Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: (a + b)B = aB + bB

If A = `[(0, -x),(x, 0)]`, B = `[(0, 1),(1, 0)]` and x² = –1, then show that (A + B)² = A² + B². 

If A = `[(1, 2),(4, 1)]`, find A² + 2A + 7I.

Matrix multiplication is ______ over addition.

Matrices of any order can be added.

If `|(2x, 5),(8, x)| = |(6, 5),(8, 3)|`, then find x