HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

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.

If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a², b², c² are in A.P.

State whether the following equation has a solution or not?

3 sin θ = 5

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

If sin^-1(1 - x) - 2 sin^-1x =  `pi/2`, then find the value of x.

If tan^-12x + tan^-13x = `pi/4`, then find the value of x.

Show that `tan^-1  1/2 - tan^-1  1/4 = tan^-1  2/9`.

Show that `cot^-1  1/3 - tan^-1  1/3 = cot^-1  3/4`.

Show that `tan^-1  1/2 = 1/3  tan^-1  11/2`

Show that `cos^-1  sqrt3/2 + 2 sin^-1  sqrt3/2 = (5pi)/6`.

Show that `2 cot^(-1)  3/2 +  sec^(-1)  13/12 = π/2`

Prove the following:

`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0

Prove the following:

`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0