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Title: class 12 cbse math ncert solved note
Description: all ans of question is provided
Description: all ans of question is provided
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Exercise 2
...
Therefore, the principal value of
...
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Let cosec−1 (2) = y
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vidhyarjan
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 6:
Find the principal value of tan−1 (−1)
Answer
Let tan−1 (−1) = y
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
We know that the range of the principal value branch of cot−1 is (0,π) and
Therefore, the principal value of
Question 9:
Find the principal value of
Answer
We know that the range of the principal value branch of cos−1 is [0,π] and
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 11:
Find the value of
Answer
Question 12:
Find the value of
Answer
Page 5 of 38
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...
We know that the range of the principal value branch of sin−1 is
Therefore,
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Page 7 of 38
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2
Question 1:
Prove
Answer
To prove:
Let x = sinθ
...
H
...
=
= 3θ
= L
...
S
...
Then, cos−1 x =θ
...
vidhyarjan
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Mobile: 9999 249717
Head Office: 1/3-H-A-2, Street # 6, East Azad Nagar, Delhi-110051
(One Km from ‘Welcome’ Metro Station)
Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 3:
Prove
Answer
To prove:
Question 4:
Prove
Answer
To prove:
Page 9 of 38
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vidhyarjan
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Mobile: 9999 249717
Head Office: 1/3-H-A-2, Street # 6, East Azad Nagar, Delhi-110051
(One Km from ‘Welcome’ Metro Station)
Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 6:
Write the function in the simplest form:
Answer
Put x = cosec θ ⇒ θ = cosec−1 x
Question 7:
Write the function in the simplest form:
Page 11 of 38
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vidhyarjan
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Head Office: 1/3-H-A-2, Street # 6, East Azad Nagar, Delhi-110051
(One Km from ‘Welcome’ Metro Station)
Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 9:
Write the function in the simplest form:
Answer
Question 10:
Write the function in the simplest form:
Answer
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Then,
Question 12:
Page 14 of 38
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Then, θ = tan−1 x
...
Then, Φ = tan−1 y
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Class XII
If
Chapter 2 – Inverse Trigonometric Functions
Maths
, then find the value of x
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Hence, the value of x is
Question 15:
If
, then find the value of x
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vidhyarjan
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Hence, the value of x is
Question 16:
Find the values of
Answer
Page 18 of 38
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Here,
Now,
can be written as:
Question 17:
Find the values of
Answer
We know that tan−1 (tan x) = x if
, which is the principal value branch of
−1
tan x
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vidhyarjan
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 18:
Find the values of
Answer
Let
...
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Mobile: 9999 249717
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Find the values of
(A)
(B)
(C)
Maths
is equal to
(D)
Answer
We know that cos−1 (cos x) = x if
, which is the principal value branch of cos
−1
x
...
Question 20:
Find the values of
(A)
(B)
(C)
is equal to
(D) 1
Answer
Let
...
Page 21 of 38
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Page 22 of 38
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Here,
Now,
can be written as:
Question 2:
Find the value of
Answer
We know that tan−1 (tan x) = x if
tan
, which is the principal value branch of
−1
x
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vidhyarjan
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Mobile: 9999 249717
Head Office: 1/3-H-A-2, Street # 6, East Azad Nagar, Delhi-110051
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 3:
Prove
Answer
Now, we have:
Page 24 of 38
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vidhyarjan
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Mobile: 9999 249717
Head Office: 1/3-H-A-2, Street # 6, East Azad Nagar, Delhi-110051
(One Km from ‘Welcome’ Metro Station)
Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 5:
Prove
Answer
Page 26 of 38
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vidhyarjan
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Mobile: 9999 249717
Head Office: 1/3-H-A-2, Street # 6, East Azad Nagar, Delhi-110051
(One Km from ‘Welcome’ Metro Station)
Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 6:
Prove
Answer
Now, we have:
Page 28 of 38
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vidhyarjan
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com
Mobile: 9999 249717
Head Office: 1/3-H-A-2, Street # 6, East Azad Nagar, Delhi-110051
(One Km from ‘Welcome’ Metro Station)
Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 8:
Prove
Answer
Page 30 of 38
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vidhyarjan
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Mobile: 9999 249717
Head Office: 1/3-H-A-2, Street # 6, East Azad Nagar, Delhi-110051
(One Km from ‘Welcome’ Metro Station)
Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 10:
Prove
Answer
Question 11:
Prove
[Hint: putx = cos 2θ]
Answer
Page 32 of 38
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vidhyarjan
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Mobile: 9999 249717
Head Office: 1/3-H-A-2, Street # 6, East Azad Nagar, Delhi-110051
(One Km from ‘Welcome’ Metro Station)
Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
Question 13:
Solve
Answer
Question 14:
Solve
Answer
Page 34 of 38
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Then,
The correct answer is D
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Class XII
(A)
Chapter 2 – Inverse Trigonometric Functions
(B)
Maths
(C) 0 (D)
Answer
Therefore, from equation (1), we have
Put x = sin y
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Class XII
Chapter 2 – Inverse Trigonometric Functions
Maths
is not the solution of the given equation
...
Hence, the correct answer is C
...
(C)
(D)
Answer
Page 37 of 38
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Page 38 of 38
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Title: class 12 cbse math ncert solved note
Description: all ans of question is provided
Description: all ans of question is provided