HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______

Evaluate cot(tan⁻¹(2x) + cot⁻¹(2x))

Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`

Evaluate:

`sin[cos^-1 (3/5)]`

Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`

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

If tan⁻¹x + tan⁻¹y + tan⁻¹z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1

Prove that sin `[tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))]` = 1

Prove that cot⁻¹(7) + 2 cot⁻¹(3) = `pi/4`

Show that `sin^-1(3/5)  + sin^-1(8/17) = cos^-1(36/85)`

Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`

Find the distance between the parallel lines `x/2 = y/(-1) = z/2` and `(x - 1)/2 = (y - 1)/(-1) = (z - 1)/2`

`int (sinx)/(1 + sin x)  "d"x`

`int 1/(4x + 5x^(-11))  "d"x`

`int (sin(x - "a"))/(cos (x + "b"))  "d"x`

`int 1/sqrt(2x^2 - 5)  "d"x`

`int ["cosec"(logx)][1 - cot(logx)]  "d"x`

`int (cos2x)/(sin^2x cos^2x)  "d"x`

`int sin4x cos3x  "d"x`

`int ("e"^xlog(sin"e"^x))/(tan"e"^x)  "d"x`