RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Miscellaneous Exercise

Rajasthan Board RBSE Class 12 Maths Chapter 2 Inverse Circular Functions Miscellaneous Exercise

RBSE Solutions For Class 12 Maths Chapter 2 Miscellaneous Question 1.
Principal value of tan^-1(- 1) is :
(a) 45°
(b) 135°
(c) – 45°
(d) – 60°
Solution:
∵ tan^-1(- x)= – tan^-1 x
tan^-1 (-1) = – tan^-1(1)
Let tan^-11 = θ
∴ tan θ = 1
⇒ tan θ = tan 45°
∴ θ = 45°
∴ tan^-1(-1) = – 45°
So, option (c) correct.

RBSE Class 12 Maths Chapter 2 Miscellaneous Question 2.
2 tan^-1(1/2) is equal to :

Solution:

So, option (a) is correct.

RBSE Solutions For Class 12 Maths Chapter 2 Question 3.
If tan^-1 (3/4) = θ, then sin is :

Solution:
According to question,

RBSE Solution Class 12 Maths Chapter 2 Question 4.
cot (tan^-1 α + cot^-1 α) is equal to:
(a) 1
(b) ∞
(c) 0
(d) none of those
Solution:
cos (tan^-1 a + cot^-1 a)

So, option (c) correct.

Class 12 Maths RBSE Solution Chapter 2 Question 5.
If sin^-1 ( \(\frac { 1 }{ 2 }\) ) = x, then general value of x is :

Solution:
Given,

Hence, option (d) is correct.

RBSE Solutions For Class 12 Maths Chapter 2 Example Question 6.
2 tan (tan^-1x + tan^-1 x³) is :

Solution:

Hence, option (a) is correct.

Miscellaneous Exercise 2 Class 12 Question 7.
If tan^-1(3x) + tan^-1 (2x) = \(\frac { \pi }{ 4 }\), then x is:

Solution:

RBSE Class 12 Maths Chapter 2 Question 8.
Value of sin^-1( \(\frac { \sqrt { 3 } }{ 2 }\) ) + 2 cos^-1 (\(\frac { \sqrt { 3 } }{ 2 }\) )is :

Solution:

Inverse Circular Functions Class 12 RBSE Question 9.
If tan^-1(1) + cos^-1 ( \(\frac { 1 }{ \sqrt { 2 } } \)) = sin^-1 x, then value of x is:

Solution:

Misc Ex Ch 2 Class 12 Question 10.
If cot^-1 x + tan^-1 \(\frac { 1 }{ 3 }\) = \(\frac { \pi }{ 2 }\) then x is :
(a) 1
(b) 3
(c) \(\frac { 1 }{ 3 }\)
(d) none of these
Solution:

Hence, option (c) is correct.

RBSE Class 12 Maths Chapter 2 Solution Question 11.
If 4 sin^-1 x + cos^-1x = π, then find x.
Solution:
4 sin^-1x + cos^-1x = π

Class 12 Maths Chapter 2 Miscellaneous Exercise Solutions Question 12.

Solution:

Class 12 Maths Ch 2 Miscellaneous Question 13.
If sin^-1 (\(\frac { 3 }{ 4 }\) ) + sec^-1 (\(\frac { 4 }{ 3 }\) ) = x, then find x.
Solution:

Chapter 2 Maths Class 12 Question 14.
Find: sin^-1 (\(\frac { 4 }{ 5 }\)) + 2 tan^-1 (\(\frac { 1 }{ 3 }\))
Solution:

RBSE Solutions For Class 12 Maths Chapter 11 Miscellaneous Question 15.
If sin^-1(\(\frac { 5 }{ 13 }\)) + sin-1 (\(\frac { 12 }{ x }\)) = 90°, then find x.
Solution:

Miscellaneous Exercise On Chapter 2 Class 12 Question 16.
Prove that:

Solution:

Ex 2 Miscellaneous Class 12 Question 17.
tan^-1x + tan^-1y + tan^-1z = π, then prove x + y + z = xyz
Solution:
tan^-1x + tan^-1y + tan^-1z = π

Chapter 2 Class 12 Miscellaneous Question 18.
Prove that tan^-1(\(\frac { 1 }{ 2 }\) tan 2A) + tan^-1 (cot A) + tan^-1 (cot² A) = 0.
Solution:

Miscellaneous Chapter 2 Class 12 Question 19.
Prove that tan^-1x = 2 tan^-1(cosec (tan^-1 x) – tan (cot^-1 x)].
Solution:
Let tan^-1x = θ

Ch 2 Maths Class 12 Miscellaneous Question 20.
then prove that value of Φ – θ is 30°.
Solution:

Question 21.
Prove that:

Solution:

RBSE Solutions for Class 12 Maths