#### Chapters

Chapter 1.2: Matrics

Chapter 1.3: Trigonometric Functions

Chapter 1.4: Pair of Lines

Chapter 1.5: Vectors and Three Dimensional Geometry

Chapter 1.6: Line and Plane

Chapter 1.7: Linear Programming Problems

Chapter 2.1: Differentiation

Chapter 2.2: Applications of Derivatives

Chapter 2.3: Indefinite Integration

Chapter 2.4: Definite Integration

Chapter 2.5: Application of Definite Integration

Chapter 2.6: Differential Equations

Chapter 2.7: Probability Distributions

Chapter 2.8: Binomial Distribution

## Chapter 1: Trigonometric Functions

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric Functions MCQ

#### 2 marks each

The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______

`pi/3, (11pi)/6`

`pi/6, (11pi)/6`

`pi/4, (11pi)/4`

`pi/6, (11pi)/3`

In ∆ABC, if cos A = `(sin"B")/(2 sin "C")`, then ∆ABC is ______

an equilateral triangle

a right angled triangle

an isosceles triangle

an isosceles right angled triangle

sin^{−1}x − cos^{−1}x = `pi/6`, then x = ______

`1/2`

`sqrt(3)/2`

`-1/2`

`-sqrt(3)/2`

The principal value of sin^{−1}`(1/2)` is ______

`pi/3`

`pi/6`

`(2pi)/3`

`(3pi)/2`

The principal value of cos^{−1}`(-1/2)` is ______

`pi/3`

`pi/6`

`(2pi)/3`

`(3pi)/2`

In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______

`1:sqrt(3):2`

`2:sqrt(3):1`

`sqrt(3):1:2`

`sqrt(3):2:1`

In ∆ABC, if b^{2} + c^{2} − a^{2} = bc, then ∠A = ______

`pi/4`

`pi/3`

`pi/2`

`pi/6`

If polar co-ordinates of a point are `(3/4, (3pi)/4)`, then its Cartesian co-ordinate are ______

`(3/(4sqrt(2)), -3/(4sqrt(2)))`

`(3/(4sqrt(2)), 3/(4sqrt(2)))`

`(-3/(4sqrt(2)), 3/(4sqrt(2)))`

`(-3/(4sqrt(2)), -3/(4sqrt(2)))`

`tan^-1(tan (7pi)/6)` = ______

`- pi/6`

`pi/6`

`(13pi)/6`

`(5pi)/6`

If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______

`1/5`

`-1/5`

5

−5

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric Functions Very Short Answers

#### 1 Mark

Evaluate cot(tan^{−1}(2x) + cot^{−1}(2x))

In ∆ABC, prove that ac cos B − bc cos A = a^{2} − b^{2}

In ∆ABC, if sin^{2}A + sin^{2}B = sin^{2}C, then show that a^{2} + b^{2} = c^{2}

Find the polar co-ordinates of point whose Cartesian co-ordinates are `(1 sqrt(3))`

Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`

Evaluate `sin[cos^-1 (3/5)]`

In ΔABC, a = 3, b = 4 and sin A = `3/4`, find ∠B

Find the principal solutions of cosec x = 2

Find the principal solutions of sin x − 1 = 0

Find the Cartesian co-ordinates of point whose polar co-ordinates are `(4, pi/3)`

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric Functions Short Answers I

#### 2 Marks each

With usual notations, prove that `(cos "A")/"a" + (cos "B")/"b" + (cos "C")/"c" = ("a"^2 + "b"^2 + "c"^2)/(2"abc")`

Find the principal solutions of cos 2𝑥 = 1

In ∆ABC, prove that `("b" - "c")^2 cos^2 ("A"/2) + ("b" + "c")^2 sin^2 ("A"/2)` = a^{2}

Find the principal solutions of sin x = `-1/2`

Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`

In ∆ABC, if a = 13, b = 14, c = 15, then find the value of cos B

In ∆ABC, if `(cos "A")/"a" = (cos "B")/"b"`, then show that it is an isosceles triangle

Find the principal solutions of tan x = `-sqrt(3)`

Evaluate `cos[pi/6 + cos^-1 (- sqrt(3)/2)]`

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric Functions Short Answers II

#### 3 Marks

In ΔABC, if a cos A = b cos B, then prove that ΔABC is either a right angled or an isosceles triangle

In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`

If tan^{−1}x + tan^{−1}y + tan^{−1}z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1

Prove that sin `[tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))]` = 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)`

If the angles A, B, C of ΔABC are in A.P. and its sides a, b, c are in G.P., then show that a^{2}, b^{2}, c^{2} are in A.P.

Prove that cot^{−1}(7) + 2 cot^{−1}(3) = `pi/4`

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric Functions Long Answers III

#### 4 Marks

In ∆ABC, prove that `(cos^2"A" - cos^2"B")/("a" + "b") + (cos^2"B" - cos^2"C")/("b" + "c") + (cos^2"C" - cos^2"A")/("c" + "a")` = 0

Show that `sin^-1(3/5) + sin^-1(8/17) = cos^-1(36/85)`

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

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

Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`

In ∆ABC, if ∠A = `pi/2`, then prove that sin(B − C) = `("b"^2 - "c"^2)/("b"^2 + "c"^2)`

If cos^{–1}x + cos^{–1}y – cos^{–1}z = 0, then show that x^{2} + y^{2} + z^{2} – 2xyz = 1

## Chapter 1: Trigonometric Functions

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 - Trigonometric Functions

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 Trigonometric Functions are Trigonometric Equations and Their Solutions, Solutions of Triangle, Inverse Trigonometric Functions.

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