HSC Science (Computer Science) १२ वीं कक्षा - Maharashtra State Board Important Questions

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)

Find the principal solutions of cot θ = 0

Find the cartesian co-ordinates of the point whose polar co-ordinates are `(1/2, π/3)`.

If 2 tan^–1(cos x) = tan^–1(2 cosec x). then find the value of x.

Find the general solution of sin θ + sin 3θ + sin 5θ = 0

If –1 ≤ x ≤ 1, the prove that sin^–1 x + cos^–1 x = `π/2`