HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Important Questions

 In , ΔABC with usual notations prove that

(a-b)² cos² `("C"/2) +("a"+"b")^2 "sin"^2("C"/2) = "c"^2`

Find the general solution of the following equation:

sinθ = `1/2`.

Find the general solution of the following equation:

4 cos² θ  = 3

State whether the following equation has a solution or not?

2sinθ = 3

Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(sqrt(2), pi/4)`

Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(3/4, (3pi)/4)`

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

In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.

In ΔABC, if cot A, cot B, cot C are in A.P. then show that a², b², c² are also in A.P.

In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `(A/2)`.

Prove the following:

`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`

Select the correct option from the given alternatives:

The principal solutions of equation sin θ = `- 1/2` are ______.

Select the correct option from the given alternatives:

The principal solutions of equation cot θ = `sqrt3` are ______.

Select the correct option from the given alternatives:

The general solution of sec x = `sqrt(2)` is ______.

Select the correct option from the given alternatives:

If cos pθ = cos qθ, p ≠ q, then ______.

`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 ______.