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

The principal value of sin^–1 `(- sqrt3/2)` is ______.

If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.

Select the correct option from the given alternatives:

If tan^-1(2x) + tan^-1(3x) = `pi/4`, then x = _____

Select the correct option from the given alternatives:

`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____

Select the correct option from the given alternatives:

`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______

The principal value branch of sec^-1x is ______.

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

If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.

Select the correct option from the given alternatives:

In any ΔABC, if acos B = bcos A, then the triangle is

Find the principal solutions of the following equation:

sin 2θ = `-1/2`

Find the principal solutions of the following equation:

tan 3θ = - 1

Find the principal solutions of the following equation:

cot θ = 0

Find the general solutions of the following equation:

`tan theta = - sqrt3`

Find the general solutions of the following equation:

`tan^2 theta = 3`

Find the general solutions of the following equation:

sin² θ - cos² θ = 1

Find the general solutions of the following equation:

sin θ - cos θ = 1

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

With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`

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

In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.