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

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Chapters

12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 - Shaalaa.com

Chapter 1: Trigonometric Functions

MCQVery Short AnswersShort Answers IShort Answers IILong Answers III
MCQ

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

MCQ | Q 1

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`

MCQ | Q 2

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

MCQ | Q 3

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

  • `1/2`

  • `sqrt(3)/2`

  • `-1/2`

  • `-sqrt(3)/2`

MCQ | Q 4

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

  • `pi/3`

  • `pi/6`

  • `(2pi)/3`

  • `(3pi)/2`

MCQ | Q 5

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

  • `pi/3`

  • `pi/6`

  • `(2pi)/3`

  • `(3pi)/2`

MCQ | Q 6

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`

MCQ | Q 7

In ∆ABC, if b2 + c2 − a2 = bc, then ∠A = ______

  • `pi/4`

  • `pi/3`

  • `pi/2`

  • `pi/6`

MCQ | Q 8

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)))`

MCQ | Q 9

`tan^-1(tan  (7pi)/6)` = ______

  • `- pi/6`

  • `pi/6`

  • `(13pi)/6`

  • `(5pi)/6`

MCQ | Q 10

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

  • `1/5`

  • `-1/5`

  • 5

  • −5

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Very Short Answers

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

Very Short Answers | Q 1

Evaluate cot(tan−1(2x) + cot−1(2x))

Very Short Answers | Q 2

In ∆ABC, prove that ac cos B − bc cos A = a2 − b2 

Very Short Answers | Q 3

In ∆ABC, if sin2A + sin2B = sin2C, then show that a2 + b2 = c2 

Very Short Answers | Q 4

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

Very Short Answers | Q 5

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

Very Short Answers | Q 6

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

Very Short Answers | Q 7

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

Very Short Answers | Q 8

Find the principal solutions of cosec x = 2

Very Short Answers | Q 9

Find the principal solutions of sin x − 1 = 0

Very Short Answers | Q 10

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

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Short Answers I

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

Short Answers I | Q 1

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

Short Answers I | Q 2

Find the principal solutions of cos 2𝑥 = 1

Short Answers I | Q 3

In ∆ABC, prove that `("b" - "c")^2 cos^2 ("A"/2) + ("b" + "c")^2 sin^2 ("A"/2)` = a2 

Short Answers I | Q 4

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

Short Answers I | Q 5

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

Short Answers I | Q 6

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

Short Answers I | Q 7

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

Short Answers I | Q 8

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

Short Answers I | Q 9

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

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Short Answers II

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

Short Answers II | Q 1

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

Short Answers II | Q 2

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

Short Answers II | Q 3

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

Short Answers II | Q 4

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

Short Answers II | Q 5

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

Short Answers II | Q 6

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

Short Answers II | Q 7

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 a2, b2, c2 are in A.P.

Short Answers II | Q 8

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

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Long Answers III

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

Long Answers III | Q 1

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

Long Answers III | Q 2

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

Long Answers III | Q 3

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

Long Answers III | Q 4

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

Long Answers III | Q 5

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

Long Answers III | Q 6

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

Long Answers III | Q 7

If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1

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Chapter 1: Trigonometric Functions

MCQVery Short AnswersShort Answers IShort Answers IILong Answers III
12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 - Shaalaa.com

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

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