Science (English Medium) Class 12 - CBSE Question Bank Solutions

Prove the following:

3 sin⁻¹ x = sin⁻¹ (3x − 4x³), `x ∈ [-1/2, 1/2]`

Prove the following: 

3cos⁻¹x = cos⁻¹(4x³ − 3x), `x ∈ [1/2, 1]`

Prove `tan^(-1)  2/11 + tan^(-1)  7/24 = tan^(-1)  1/2`

Prove `2 tan^(-1)  1/2 + tan^(-1)  1/7 = tan^(-1)  31/17`

Write the following function in the simplest form:

`tan^(-1)  (sqrt(1+x^2) -1)/x`, x ≠ 0

Write the function in the simplest form: `tan^(-1)  1/(sqrt(x^2 - 1)), |x| > 1`

Write the following function in the simplest form:

`tan^(-1) (sqrt((1-cos x)/(1 + cos x)))`, 0 < x < π

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)/sqrt3 < x < a/sqrt3`

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 ______.