Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

If f(x) = (4 – (x – 7)³}, then f^–1(x) = ______.

Let A = {0, 1} and N be the set of natural numbers. Then the mapping f: N → A defined by f(2n – 1) = 0, f(2n) = 1, ∀ n ∈ N, is onto.

Evaluate `tan^-1(sin((-pi)/2))`.

Evaluate tan (tan^–1(– 4)).

Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.

Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`

Evaluate `cos[sin^-1  1/4 + sec^-1  4/3]`

Prove that `2sin^-1  3/5 - tan^-1  17/31 = pi/4`

Prove that cot^–17 + cot^–18 + cot^–118 = cot^–13

Solve the equation `sin^-1 6x + sin^-1 6sqrt(3)x = - pi/2`

Show that `2tan^-1 {tan  alpha/2 * tan(pi/4 - beta/2)} = tan^-1  (sin alpha cos beta)/(cosalpha + sinbeta)`

If `tan^-1x = pi/10` for some x ∈ R, then the value of cot^–1x is ______.

If α ≤ 2 sin^–1x + cos^–1x ≤ β, then ______.

Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`

Prove that `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/((1 + x^2) - sqrt(1 - x^2))) = pi/2 + 1/2 cos^-1x^2`

Prove that `sin^-1  8/17 + sin^-1  3/5 = sin^-1  7/85`

Show that `tan(1/2 sin^-1  3/4) = (4 - sqrt(7))/3` and justify why the other value `(4 + sqrt(7))/3` is ignored?

If a₁, a₂, a₃,...,a_n is an arithmetic progression with common difference d, then evaluate the following expression.

`tan[tan^-1("d"/(1 + "a"_1 "a"_2)) + tan^-1("d"/(21 + "a"_2 "a"_3)) + tan^-1("d"/(1 + "a"_3 "a"_4)) + ... + tan^-1("d"/(1 + "a"_("n" - 1) "a""n"))]`

If 3 tan^–1x + cot^–1x = π, then x equals ______.

If `sin^-1 ((2"a")/(1 + "a"^2)) + cos^-1 ((1 - "a"^2)/(1 + "a"^2)) = tan^-1 ((2x)/(1 - x^2))`. where a, x ∈ ] 0, 1, then the value of x is ______.