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    Home » NCERT Solutions Class 12 Maths Chapter 2 Inverse Trigonometric Functions
    Class 12 Math

    NCERT Solutions Class 12 Maths Chapter 2 Inverse Trigonometric Functions

    AdminBy AdminUpdated:May 9, 20236 Mins Read
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    Free NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions solved by Expert Teachers as per NCERT (CBSE) Book guidelines and brought to you by CBSE Learning. These Inverse Trigonometric Functions Exercise Questions with Solutions for Class 12 Maths covers all questions of Chapter Inverse Trigonometric Functions Class 12 and help you to revise complete Syllabus and Score More marks as per CBSE Board guidelines from the latest NCERT book for class 12 maths. You can read and download NCERT Book Solution to get a better understanding of all topics and concepts
    2.1 Introduction
    2.2 Basic Concepts
    2.3 Properties of Inverse Trigonometric Functions.

    Inverse Trigonometric Functions NCERT Solutions – Class 12 Maths

    Q1 : Find the principal value of 
    Answer :
    Let =y. Then sin y=
    We know that the range of the principal value branch of sin-1 is
    and sin
    Therefore, the principal value of


    Q2 : Find the principal value of
    Answer :
    We know that the range of the principal value branch of cos -1is

    Therefore, the principal value of.


    Q3 : Find the principal value of cosec-1(2)
    Answer :
    Let cosec -1(2) = y. Then,
    We know that the range of the principal value branch of cosec-1is
    Therefore, the principal value of


    Q4 : Find the principal value of
    Answer :
    We know that the range of the principal value branch of tan -1is

    Therefore, the principal value of


    Q5 : Find the principal value of
    Answer :
    We know that the range of the principal value branch of cos -1is

    Therefore, the principal value of


    Q6 : Find the principal value of tan-1(-1)
    Answer :
    Let tan-1(-1) = y. Then,
    We know that the range of the principal value branch of tan-1 is
    Therefore, the principal value of


    Q7 : Find the principal value of
    Answer :
    We know that the range of the principal value branch of sec-1 is

    Therefore, the principal value of


    Q8 :Find the principal value of
    Answer :
    We know that the range of the principal value branch of cot-1 is
    (0,π) and
    Therefore, the principal value of


    Q9 : Find the principal value of
    Answer :
    We know that the range of the principal value branch of cos-1 is [0,π] and

    Therefore, the principal value of


    Q10 : Find the principal value of
    Answer :
    We know that the range of the principal value branch of cosec-1 is
    Therefore, the principal value of


    Q11 :Find the value of
    Answer :


    Q12 :Find the value ofAnswer :


    Q13 :Find the value of if sin – 1 x = y, then
    (A) (B)
    (C) (D)
    Answer :
    It is given that sin-1 x = y.
    We know that the range of the principal value branch of sin-1 is
    Therefore,.


    Q14 :Find the value of is equal to
    (A) π (B) (C) (D)
    Answer


    Exercise 2.2 : Solutions of Questions on Page Number : 47
    Q1 :Prove
    Answer :
    To prove:
    Let x = sinθ. Then,
    We have,
    R.H.S. =

    = 3θ

    = L.H.S.


    Q2 :Prove
    Answer :
    To prove:
    Let x = cosθ. Then, cos-1 x =θ.
    We have,


    Q3 :Prove
    Answer :
    To prove:


    Q4 :Prove
    Answer :
    To prove:


    Q6 :Write the function in the simplest form:

    Answer :
    Put x = cosec θ ⇒ θ = cosec-1 x


    Q7 :Write the function in the simplest form:
    Answer :


    Q8 :Write the function in the simplest form:

    Answer :


    Q9 :Write the function in the simplest form:

    Answer :


    Q10 :Write the function in the simplest form:

    Answer :


    Q11 :Find the value of
    Answer :
    Let. Then,


    Q12 :Find the value of
    Answer :


    Q13 :Find the value of

    Answer :
    Let x = tan θ. Then, θ = tan-1 x.

    Let y = tan Φ. Then, Φ = tan-1 y.


    Q14 :If, then find the value of x.
    Answer :

    On squaring both sides, we get:

    Hence, the value of x is


    Q15 :If, then find the value of x.
    Answer :

    Hence, the value of x is


    Q16 :Find the values of
    Answer :

    We know that sin-1 (sin x) = x if, which is the principal value branch of sin-1 x.
    Here,
    Now, can be written as:


    Q17 :Find the values of
    Answer :
    We know that tan-1 (tan x) = x if, which is the principal value branch of tan-1x.
    Here,
    Now, can be written as:


    Q18 :Find the values of
    Answer :
    Let. Then,


    Q19 :Find the values of is equal to
    (A) (B) (C) (D)
    Answer :
    We know that cos-1 (cos x) = x if, which is the principal value branch of cos-1 x.
    Here,
    Now, can be written as:
    The correct answer is B.


    Q20 :Find the values of  is equal to

    Answer :
    Let . Then 
    We know that the range of the principle value branch of 


    The correct answer is D.


    Q21 :Find the values of is equal to
    (A) π (B) (C) 0 (D)
    Answer :
    Let. Then,
    We know that the range of the principal value branch of Let.
    The range of the principal value branch of The correct answer is B.


    Exercise Miscellaneous : Solutions of Questions on Page Number : 51


    Q1 :Find the value of
    Answer :
    We know that cos-1 (cos x) = x if, which is the principal value branch of cos-1 x.
    Here,
    Now, can be written as:


    Q2 :Find the value of
    Answer :
    We know that tan-1 (tan x) = x if, which is the principal value branch of tan-1 x.
    Here,
    Now, can be written as:


    Q3 :Prove
    Answer :

    Now, we have:


    Q4 :Prove
    Answer :

    Now, we have:


    Q5 :Prove
    Answer :

    Now, we will prove that:


    Q6 :Prove
    Answer :

    Now, we have:


    Q7 :Prove
    Answer :

    Using (1) and (2), we have


    Q8 :Prove
    Answer :


    Q9 :Prove
    Answer :


    Q10 :Prove
    Answer :


    Q11 :Prove [Hint: putx = cos 2θ]
    Answer :


    Q12 :Prove
    Answer :


    Q13 :Solve
    Answer :


    Q14: Solve 
    Answer:

    Q15 :Solveis equal to
    (A) (B) (C) (D)
    Answer :
    Let tan – 1 x = y. Then,

    The correct answer is D.


    Q16 :Solve, then x is equal to
    (A) (B) (C) 0 (D)
    Answer :

    Therefore, from equation (1), we have

    Put x = sin y. Then, we have:

    But, when, it can be observed that:

    is not the solution of the given equation.
    Thus, x = 0.
    Hence, the correct answer is C.


    Q17 :Solve is equal to
    (A) (B) (C) (D)
    Answer :

    Hence, the correct answer is C.

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    Previous ArticleNCERT Solutions Class 12 Maths Chapter 1 Relations and Functions
    Next Article NCERT Solutions Class 12 Maths Chapter 3 Matrices

    Class 12 Maths Chapter Solutions

    • Chapter 1 - Relations and Functions
    • Chapter 2 - Inverse Trigonometric Functions
    • Chapter 3 - Matrices
    • Chapter 4 - Determinants
    • Chapter 5 - Continuity and Differentiability
    • Chapter 6 - Application of Derivatives
    • Chapter 7 - Integrals
    • Chapter 8 - Application of Integrals
    • Chapter 9 - Differential Equations
    • Chapter 10 - Vector Algebra
    • Chapter 11 - Three Dimensional Geometry
    • Chapter 12 - Linear Programming
    • Chapter 13 - Probability
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