RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1

Rajasthan Board RBSE Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1

RBSE Solutions For Class 12 Maths Chapter 2 Question 1.
Find the principal value of the following angles:
RBSE Solutions For Class 12 Maths Chapter 2 Inverse Circular Functions
Solution:
(i) sin-1(1)
RBSE Solution Class 12 Maths Chapter 2 Inverse Circular Functions
Inverse Circular Functions Class 12 RBSE
RBSE Class 12 Maths Chapter 2 Inverse Circular Functions
RBSE Solutions For Class 12 Maths Chapter 2.1 Inverse Circular Functions

Prove the following : (Q. 2 to 8)
RBSE Solution Class 12 Maths Chapter 2 Question 2.
RBSE Solutions For Class 12 Maths Chapter 2 Miscellaneous Inverse Circular Functions
Solution:
Class 12 Maths RBSE Solution Chapter 2 Inverse Circular Functions

Question 3.
RBSE Solution 12th Math Chapter 2 Inverse Circular Functions
Solution:
12th Maths Exercise 2.1 Inverse Circular Functions

Inverse Circular Functions Class 12 RBSE Question 4.
Maths RBSE Solutions Class 12 Inverse Circular Functions
Solution:
RBSE Solution 12th Class Inverse Circular Functions
12th Maths RBSE Solution Inverse Circular Functions

RBSE Class 12 Maths Chapter 2 Question 5.
sec2 (tan-1 2) + cosec2 (cot-1 3) = 15
Solution:
Let tan-12 = θ
⇒ tan θ = 2
sec2 θ = 1 + tan2 θ
= 1 + (2)2
= 1 + 4 = 5
∴ sec2 (tan-12) = 5
Let cot-13 = Φ = cot Φ = 3
∴ cosec2 Φ = 1 + cot2 Φ
= 1 + (3)2 = 1 + 9 = 10
∴ cosec2(cot-1 3) = 10 …..(ii)
Adding eq. (i) and (ii), we get
sec2 (tan-12) + cosec2 (cot-13) = 5 + 10
⇒ sec2 (tan-12) + cosec2(cot-13) = 15
Hence proved.

RBSE Solutions For Class 12 Maths Chapter 2.1 Question 6.
Class 12 Hindi RBSE Solutions Inverse Circular Functions
Solution:
RBSE Solution Class 12th English Inverse Circular Functions
12th RBSE Solutions Inverse Circular Functions

RBSE Solutions For Class 12 Maths Chapter 2 Miscellaneous Question 7.
RBSE Solutions Of Class 12 Inverse Circular Functions
Solution:
12th Class RBSE Solution Inverse Circular Functions

Class 12 Maths RBSE Solution Chapter 2 Question 8.
RBSE Solutions For Class 12 Maths Inverse Circular Functions
Solution:
RBSE Solution Class 12 Hindi Inverse Circular Functions
RBSE Solution For Class 12th

RBSE Solution 12th Math Question 9.
If cos-1x + cos-1y + cos-1z = π, then prove that x2 + y2 + x2 + 2xyz = 1. Solution:
cos-1x + cos-1y + cos-1z = π
(According to question)
cos-1x + cos-1 y = π – cos-1z
RBSE Solution Class 12th Maths Inverse Circular Functions

12th Maths Exercise 2.1 Question 10.
If sin-1x + sin-1 y + sin-1z = π, then prove that:
12 Class RBSE Solution Chapter 2 Inverse Circular Functions
Solution:
Let sin-1 x = A ⇒ x = sin A
sin-1 y = B ⇒ y = sin B
sin-1 z = C ⇒ z = sin C
∵ sin-1 x + sin-1 y + sin-1 z = π
∴ A + B + C = π
∴ To prove
RBSE Solution Of Class 12th Chapter 2 Inverse Circular Functions
RBSE Solutions 12 Maths Chapter 2 Inverse Circular Functions

Maths RBSE Solutions Class 12 Question 11.
If tan-1x + tan-1y + tan-1z = π/2, then prove that xy + yz + zx = 1.
Solution:
According to question,
RBSE Solutions For Class 12 Maths Chapter 2 Inverse Circular Functions

RBSE Solution 12th Class Question 12.
If
12th Math RBSE Solutions Chapter 2 Inverse Circular Functions
then prove that x + y + z = xyz.
Solution:
Let x = tan A, y = tan B, z = tan C
12th RBSE Solution Chapter 2 Inverse Circular Functions
Class 12 Maths RBSE Solutions Chapter 2 Inverse Circular Functions

12th Maths RBSE Solution Question 13.
If
12 Maths RBSE Solution Chapter 2 Inverse Circular Functions
then prove that x + y + z = xyz.
Solution:
According to question
RBSE Solutions For Class 12th English Chapter 2 Inverse Circular Functions

Class 12 Hindi RBSE Solutions Question 14.
Prove that :
tan-1x + cot-1(x + 1) = tan-1(x2 + x + 1).
Solution:
L.H.S. = tan-1x + cot-1(x + 1)
12th RBSE Solution Maths Chapter 2 Inverse Circular Functions

RBSE Solution Class 12th English Question 15.
If tan-1x, tan-1y, tan-1z are in arithmetic progression, then prove that
y2(x +z) + 2y(1 – xz) – x – z = 0.
Solution:
tan-1x, tan-1y, tan-1z are in A.P.
12th RBSE Maths Solution Chapter 2 Inverse Circular Functions

12th RBSE Solutions Question 16.
If α, β, γ be the roots of equation x3 + px2 + qx + p = 0, then prove that, except a special condition,
tan-1α + tan-1 β + tan-1γ = nπ also find the special condition, when it does so on.
Solution:
Given, α, β, γ are root of equation x3+ px2 + qx + p = 0
RBSE Solution 12th Chapter 2 Inverse Circular Functions
English Class 12 RBSE Solutions Chapter 2 Inverse Circular Functions
Special Situation: When sum and product of roots is not equal, then tan-1 α + tan-1 β + tan-1γ ≠ nπ

Solve the following euqations : (Q. 17 to 25)

RBSE Solutions Of Class 12 Question 17.
RBSE 12th Maths Paper 2020 Solution Chapter 2 Inverse Circular Functions
Solution:
RBSE Solutions 12th Hindi Chapter 2 Inverse Circular Functions
Hindi Class 12 RBSE Solutions Chapter 2 Inverse Circular Functions

12th Class RBSE Solution Question 18.
RBSE Class 12 Maths Chapter 2 Inverse Circular Functions
Solution:
Class 12 RBSE Solution Chapter 2 Inverse Circular Functions

RBSE Solutions For Class 12 Maths Question 19.
Class 12th RBSE Solution Chapter 2 Inverse Circular Functions
Solution:
Maths Class 12 RBSE Solutions Chapter 2 Inverse Circular Functions
Class 12th RBSE Maths Solution Chapter 2 Inverse Circular Functions

RBSE Solution Class 12 Hindi Question 20.
RBSE Solutions For Class 12th Hindi Chapter 2 Inverse Circular Functions
Solution:
RBSE Solutions Class 12 Maths Chapter 2 Inverse Circular Functions
RBSE Maths Solution Class 12 Chapter 2 Inverse Circular Functions

RBSE Solution For Class 12th Question 21.
RBSE Solution Class 12th Chemistry Chapter 2 Inverse Circular Functions
Solution:
RBSE Solutions Chemistry Class 12 Chapter 2 Inverse Circular Functions
Class 12 English RBSE Solutions Chapter 2 Inverse Circular Functions

RBSE Solution Class 12th Maths Question 22.
Ex 2.1 Class 12 Chapter 2 Inverse Circular Functions
Solution:
12th Math RBSE Chapter 2 Inverse Circular Functions
RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1

12 Class RBSE Solution Question 23.
sin 2 (cos-1 {cot (2 tan-1x)} = 0
Solution:
Given equation
RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1
RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1

RBSE Solution Of Class 12th Question 24.
RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1
Solution:
RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1
RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1

RBSE Solutions 12 Maths Question 25.
RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1
Solution:
According to question,
RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1
RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1

RBSE Solutions for Class 12 Maths