Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions are part of Plus Two Maths Chapter Wise Questions and Answers. Here we have given Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus Two |

Subject | Maths Chapter Wise Questions |

Chapter | Chapter 2 |

Chapter Name | Inverse Trigonometric Functions |

Number of Questions Solved | 47 |

Category | Plus Two Kerala |

## Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

** Short Answer Type Questions**

**(Score 3)**

Question 1.

Show that

Answer.

Question 2.

Solve 2 tan^{-1} (cosx) = tan^{-1 }(2 cos x).

Answer.

2tan^{-1} (cosx) = tan^{-1} (2cosx)

Question 3.

i. The principal value of

ii. Show that

Answer.

Question 4.

Determine whether the statement is true or false. Justify your answer.

Answer.

(i) False. is not in the range of the inverse of sine

(ii) False is not in the range of the inverse of tan.

Question 5.

i. cos^{-1} {cos(x-θ)} =____

ii. Simplify

Answer.

i. x-θ

ii.

Question 6.

Prove that

Answer.

Question 7.

(i) Which of the following can be the value of cosec^{-1}x ?

(ii)Prove that cosec^{-1}x + sec^{-1}x =

Answer.

Question 8.

i. sin [tan^{-1}(x²) + cot^{-1} (x²) =……..

ii. Comment upon the statement

(sin x²) = sin^{-2} x

iii. Evaluate sec² (tan^{-1} 2).

Answer.

i.

ii. sin^{-1} x is a function. -1 is not the power of sin x . So the gives statement is not true.

iii. sec² (tan^{-1} 2) = 1 + tan² (tan^{-1} 2)

Question 9.

If

Answer.

Question 10.

The values of

Answer.

**Long Answer Type Questions**

**(Score 4)**

Question 1.

Show that

Answer.

Question 2.

If y = (tan^{-1} x)², show that (x² + 1)²y_{2} + 2x(x² + 1)y_{1} = 2

Answer.

Question 3.

Given x² = cos2θ

i. Write down θ using the inverse of cosine

ii. Show that

iii. Write

in the simplest form

Answer.

i. x² = cos2θ

⇒ 2θ = cos^{-1} x²

Question 4.

(i) tan^{-1} x + tan^{-1} = ……….

(ii) sin^{-1 }(sinθ) = ……..

(iii) Prove that sin^{-1} (2x√1 – x²) = 2sin^{-1} x

Answer.

Question 5.

Match the following:

Answer.

Question 6.

Show that

Answer.

Question 7.

i. Write one branch of sin^{-1}x other than principal branch.

ii. Write the simplest form of

Answer.

Question 8.

i. Which of the following can be the value of cosec^{-1} x ?

ii. Prove that cosec^{-1} x + sec^{-1} x =

Answer.

Question 9.

If cos^{-1}(x/a) + cos^{-1}(y/b) = α, prove that

Answer.

Question 10.

i. Choose the correct statement among the following:

[sin^{-1}(sin 150°) = 15°; sin^{-1}(sin2^{c}) = 2^{c}; cos^{-1}(cos2^{c}) = 2^{c}; sin^{-1}(cosθ) = cos^{-1}(sinθ)]

ii. Find the value of sin

iii. The value of cos(2tan^{-1}(-7)) is

Answer.

i. sin^{-1}(cosθ) = cos^{-1}(sinθ)

**Very Long Answer Type Questions**

**(Score 6)**

Question 1.

i. find the value of

ii. sin^{-1} sinx = x if and only if

a. x ∈R

b.

c. x ∈[-1,1]

d. x ∈(0,π)

iii. show that

Answer.

Question 2.

Answer.

Question 3.

Answer.

Question 4.

a. The principle value of sin

b. Solve cot(tan^{-1}(x) + cot^{-1} (x))

Answer.

Question 5.

a.Prove that

b. Solve 2tan^{-1} (cosx) = tan^{-1} (2 cosecx)

Answer.

Question 6.

Show that

Answer.

Question 7.

a Prove that

b. Prove that

Answer.

Question 8.

a. Find

b. Show that

Answer.

a. The principal value branch of cos^{-1} is [0,π]

Question 9.

If

,then find the value of x.

Answer.

Question 10.

Prove that

Answer.

**Edumate Questions & Answers**

Question 1.

i. Choose the correct answer from the bracket

If cos^{-1} x = y,then y is equal to

Answer.

i. Range of cos^{-1 }x is[0,π]

⇒0≤y≤π (1)

ii. cos^{-1} (cosx) = x, if x∉[0,π] which is the Principal value branch of cos^{-1}x

Question 2.

i. Choose the correct answer from the bracket

ii. prove that

Answer.

Question 3.

Match the following

Answer.

Question 4.

i. Choose the correct answer from the bracket is equal to

ii. Express in the simplest form

Answer.

Question 5.

Prove that

Answer.

Question 6.

i. In which quadrants are the graph of cos^{-1}x lies, x ∉ [-1,1]

ii. Choose the correct answer from the bracket. If cos^{-1}x + cos^{-1}y = ,

the sin^{-1}x + sin^{-1}y = ……

iii. If tan^{-1} x + tan^{-1} y = then prove that x + y + xy = 1.

Answer.

i. First and Second quadrants

Question 7.

Find the value?

Answer.

Question 8.

Evaluate

Answer.

Question 9.

Prove that

Answer.

Question 10.

i. The principal value of tan^{-1}(-1) = ……

ii. If tan^{-1} 2 + tan^{-1} 3 = x, find x in radian

Answer.

Question 11.

Find the principal value of

Answer.

Question 12.

Prove:

Answer.

Question 13.

Show that

Answer.

Let x = a sinθ. Then θ = sin^{-1} (x/a)

Question 14.

a. The principal value of

b. In proving the result 3sin ^{-1}x = sin^{-1} (3x – 4x^{3})

i. Substitute x =………

ii. Prove the result.

Answer.

a.

b. (i) x = sinθ

(ii) θ = sin^{-1}x

sin^{-1}(3x – 4x^{3}) = sin^{-1}(3sinθ – 4sinθ)

= sin^{-1}(sin3θ) = 3θ

= 3sin^{-1} x

Question 15.

Within the domain of definitions prove that sin^{-1}(-x) = – sin^{-1}x.

Answer.

Let sin^{-1}(-x) = θ………(1)

Then -x = sinθ

⇒ x = -sinθ

⇒ x

= sin(-θ)

⇒ -θ = sin^{-1}x

⇒ θ = – sin^{-1}x (2)

By (1) and (2) sin^{-1}(-x) = -sin^{-1}x

Question 16.

(i) tan^{-1}(tanθ) = …….

(ii) Show that

is independent of trigonometric functions.

Answer.

i. θ

Question 17.

Prove that

Answer.

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