HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

`cos[tan^-1  1/3 + tan^-1  1/2]` = ______

Find the principal solutions of the following equation:

sin 2θ = `-1/2`

In ΔABC, prove the following:

`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`

If | x | < 1, then prove that

`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`

In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______.

If polar co-ordinates of a point are `(3/4, (3pi)/4)`, then its Cartesian co-ordinate are ______

Evaluate cot(tan⁻¹(2x) + cot⁻¹(2x))

Find the polar co-ordinates of point whose Cartesian co-ordinates are `(1, sqrt(3))`

Find the principal solutions of cosec x = 2

In ∆ABC, if a = 13, b = 14, c = 15, then find the value of cos B

In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`

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

In ∆ABC, if `(2cos "A")/"a" + (cos "B")/"b" + (2cos"C")/"c" = "a"/"bc" + "b"/"ca"`, then show that the triangle is a right angled

In ∆ABC, prove that `sin  ((A - B)/2) = ((a - b)/c) cos  C/2` 

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

In ΔABC, prove that `("a"^2sin("B" - "C"))/(sin"A") + ("b"^2sin("C" - "A"))/(sin"B") + ("c"^2sin("A" - "B"))/(sin"C")` = 0

In ΔABC, prove that `("b"^2 - "c"^2)/"a" cos"A" + ("c"^2 - "a"^2)/"b" cos"B" + ("a"^2 - "b"^2)/"c" cos "C"` = 0

If f(x) = x⁵ + 2x – 3, then (f^–1)¹ (–3) = ______.

Find the principal value of `cot^-1 ((-1)/sqrt(3))`

If f'(x) = x^–1, then find f(x)