#### Online Mock Tests

#### 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 FunctionsMCQ

#### 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 FunctionsVery 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 FunctionsShort 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 FunctionsShort 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 FunctionsLong 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

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 (Trigonometric Functions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. SCERT Maharashtra Question Bank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Trigonometric Functions exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in SCERT Maharashtra Question Bank Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exam.

Get the free view of chapter 1 Trigonometric Functions 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 and can use Shaalaa.com to keep it handy for your exam preparation