HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos  "A"/(2)`.

With the usual notations prove that `2{asin^2  "C"/(2) + "c"sin^2  "A"/(2)}` = a – b + c.

In Δ ABC, prove that a³ sin(B – C) + b³sin(C – A) + c³sin(A – B) = 0

In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.

With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a² + b² + c² .

Differentiate the following w.r.t. x:

(x³ – 2x – 1)⁵

Differentiate the following w.r.t.x:

`(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`

Differentiate the following w.r.t. x: `sqrt(x^2 + 4x - 7)`.

Differentiate the following w.r.t.x:

`sqrt(x^2 + sqrt(x^2 + 1)`

Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`

Differentiate the following w.r.t.x:

`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`

Differentiate the following w.r.t.x: cos(x² + a²)

Differentiate the following w.r.t.x:

`sqrt(e^((3x + 2) +  5)`

Differentiate the following w.r.t.x: `log[tan(x/2)]`

Differentiate the following w.r.t.x: `sqrt(tansqrt(x)`

Differentiate the following w.r.t.x: cot³[log(x³)]

Differentiate the following w.r.t.x: `5^(sin^3x + 3)`

Differentiate the following w.r.t.x: `"cosec"(sqrt(cos x))`

Differentiate the following w.r.t.x: log[cos(x³ – 5)]

Differentiate the following w.r.t.x: `e^(3sin^2x - 2cos^2x)`