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

Write the function in the simplest form:  `tan^(-1)  ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`

Write the following function in the simplest form:

`tan^(-1)  x/(sqrt(a^2 - x^2)), |x| < a`

Write the following function in the simplest form:

`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt(3) < x < a/sqrt(3)`

Find the value of the following:

`tan^-1 [2 cos (2  sin^-1  1/2)]`

Find the value of `cot(tan^(-1) a + cot^(-1) a)`

Find the value of the following:

`tan  1/2 [sin^(-1)  (2x)/(1 + x^2) + cos^(-1)  (1 - y^2)/(1 + y^2)], |x| < 1, y > 0 and xy < 1`

if `sin(sin^(-1)  1/5 + cos^(-1) x)  = 1` then find the value of x

if `tan^(-1)  (x-1)/(x - 2) + tan^(-1)  (x + 1)/(x + 2) = pi/4` then find the value of x.

Find the value of the given expression.

`sin^(-1) (sin  (2pi)/3)`

Find the value of the given expression.

`tan^(-1) (tan  (3pi)/4)`

Find the value of the given expression.

`tan(sin^(-1)  3/5 + cot^(-1)  3/2)`

`cos^(-1) (cos  (7pi)/6)` is equal to ______.

`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.

Prove that `sin^(-1)  8/17 + sin^(-1)  3/5 = tan^(-1)  77/36`.

Prove that `cos^(-1)  4/5 + cos^(-1)  12/13 = cos^(-1)  33/65`.

Prove that `cos^(-1)  12/13 + sin^(-1)  3/5 = sin^(-1)  56/65`.

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) sqrt(x) = 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 ∈ (0, pi/4)`.