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

Find the principal value of the following: cos^{- 1}`(-1/2)`

Evaluate the following:

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

Evaluate the following:

`cos^-1(1/2) + 2sin^-1(1/2)`

Evaluate the following:

`tan^-1 sqrt(3) - sec^-1 (-2)`

Evaluate the following:

`"cosec"^-1(-sqrt(2)) + cot^-1(sqrt(3))`

Prove the following: 

`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3π)/(4)`

Prove the following:

`sin^-1(-1/2) + cos^-1(-sqrt(3)/2) = cos^-1(-1/2)`

Prove the following:

`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`

Prove the following:

`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`

Prove the following:

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

Prove the following: 

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

Prove the following:

`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`

Prove the following:

`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).

A table of values of f, g, f' and g' is given :

If r(x) =f [g(x)] find r' (2).

A table of values of f, g, f' and g' is given :

If R(x) =g[3 + f(x)] find R'(4).

A table of values of f, g, f' and g' is given:

If s(x) = f[9 − f (x)] find s'(4).

A table of values of f, g, f' and g' is given :

If S(x) =g [g(x)] find S'(6).

Assume that `f'(3) = -1,"g"'(2) = 5, "g"(2) = 3 and y = f["g"(x)], "then" ["dy"/"dx"]_(x = 2) = ?`

If h(x) = `sqrt(4f(x) + 3"g"(x)), f(1) = 4, "g"(1) = 3, f'(1) = 3, "g"'(1) = 4, "find h"'(1)`.

Find the x co-ordinates of all the points on the curve y = sin 2x − 2 sin x, 0 ≤ x < 2π, where `"dy"/"dx"` = 0.