RBSE Solutions for Class 12 Maths Chapter 2 Inverse Circular Functions Miscellaneous Exercise are part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Class 12 Maths Chapter 2 Inverse Circular Functions Miscellaneous Exercise.

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

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^{-1}1 = θ

∴ tan θ = 1

⇒ tan θ = tan 45°

∴ θ = 45°

∴ tan^{-1}(-1) = – 45°

So, option (c) correct.

Question 2.

2 tan^{-1}(1/2) is equal to :

Solution:

So, option (a) is correct.

Question 3.

If tan^{-1} (3/4) = θ, then sin is :

Solution:

According to question,

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.

Question 5.

If sin^{-1} ( \(\frac { 1 }{ 2 }\) ) = x, then general value of x is :

Solution:

Given,

Hence, option (d) is correct.

Question 6.

2 tan (tan^{-1}x + tan^{-1} x^{3}) is :

Solution:

Hence, option (a) is correct.

Question 7.

If tan^{-1}(3x) + tan^{-1} (2x) = \(\frac { \pi }{ 4 }\), then x is:

Solution:

Question 8.

Value of sin^{-1}( \(\frac { \sqrt { 3 } }{ 2 }\) ) + 2 cos^{-1} (\(\frac { \sqrt { 3 } }{ 2 }\) )is :

Solution:

Question 9.

If tan^{-1}(1) + cos^{-1} ( \(\frac { 1 }{ \sqrt { 2 } } \)) = sin^{-1} x, then value of x is:

Solution:

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.

Question 11.

If 4 sin^{-1} x + cos^{-1}x = π, then find x.

Solution:

4 sin^{-1}x + cos^{-1}x = π

Question 12.

Solution:

Question 13.

If sin^{-1} (\(\frac { 3 }{ 4 }\) ) + sec^{-1} (\(\frac { 4 }{ 3 }\) ) = x, then find x.

Solution:

Question 14.

Find: sin^{-1} (\(\frac { 4 }{ 5 }\)) + 2 tan^{-1} (\(\frac { 1 }{ 3 }\))

Solution:

Question 15.

If sin^{-1}(\(\frac { 5 }{ 13 }\)) + sin-1 (\(\frac { 12 }{ x }\)) = 90°, then find x.

Solution:

Question 16.

Prove that:

Solution:

Question 17.

tan^{-1}x + tan^{-1}y + tan^{-1}z = π, then prove x + y + z = xyz

Solution:

tan^{-1}x + tan^{-1}y + tan^{-1}z = π

Question 18.

Prove that tan^{-1}(\(\frac { 1 }{ 2 }\) tan 2A) + tan^{-1} (cot A) + tan^{-1} (cot^{2} A) = 0.

Solution:

Question 19.

Prove that tan^{-1}x = 2 tan^{-1}(cosec (tan^{-1} x) – tan (cot^{-1} x)].

Solution:

Let tan^{-1}x = θ

Question 20.

then prove that value of Φ – θ is 30°.

Solution:

Question 21.

Prove that:

Solution:

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