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

Prove that:

`tan^(-1)  63/16 = sin^(-1)  5/13 + cos^(-1)  3/5`

Prove `tan^(-1)   1/5 + tan^(-1)  (1/7) + tan^(-1)  1/3 + tan^(-1)  1/8 = pi/4`

Prove that:

`tan^(-1) sqrtx = 1/2 cos^(-1)  (1-x)/(1+x)`, x ∈ [0, 1]

Prove that:

`cot^(-1)  ((sqrt(1+sin x) + sqrt(1-sinx))/(sqrt(1+sin x) - sqrt(1- sinx))) = x/2, x in (0, pi/4)`

Prove `(9pi)/8 - 9/4  sin^(-1)  1/3 = 9/4 sin^(-1)  (2sqrt2)/3`

Solve the following equation:

2 tan⁻¹ (cos x) = tan⁻¹ (2 cosec x)

sin (tan^–1 x), |x| < 1 is equal to ______.

sin^–1 (1 – x) – 2 sin^–1 x = `pi/2`, then x is equal to ______.

Solve  `tan^(-1) -  tan^(-1)  (x - y)/(x+y)` is equal to

(A) `pi/2`

(B). `pi/3` 

(C) `pi/4` 

(D) `(-3pi)/4`

Find the adjoint of the matrices.

`[(1,2),(3,4)]`

Find the adjoint of the matrices.

`[(1,-1,2),(2,3,5),(-2,0,1)]`

Verify A(adj A) = (adj A)A = |A|I.

`[(2,3),(-4,-6)]`

Verify A(adj A) = (adj A)A = |A|I.

`[(1,-1,2),(3,0,-2),(1,0,3)]`

Find the inverse of the matrices (if it exists).

`[(2,-2),(4,3)]`

Find the inverse of the matrices (if it exists).

`[(-1,5),(-3,2)]`

Find the inverse of the matrices (if it exists).

`[(1,2,3),(0,2,4),(0,0,5)]`

Find the inverse of the matrices (if it exists).

`[(1,0,0),(3,3,0),(5,2,-1)]`

Find the inverse of the matrices (if it exists).

`[(2,1,3),(4,-1,0),(-7,2,1)]`

Find the inverse of the matrices (if it exists).

`[(1,-1,2),(0,2,-3),(3,-2,4)]`

Find the inverse of the matrices (if it exists).

`[(1,0,0),(0, cos alpha, sin alpha),(0, sin alpha, -cos alpha)]`