In this article, we share MP Board Class 12th Maths Book Solutions Chapter 2 Inverse Trigonometric Functions Ex 2.2 Pdf, These solutions are solved by subject experts from the latest MP Board books.

## MP Board Class 12th Maths Solutions Chapter 2 Inverse Trigonometric Functions Ex 2.2

Question 1.

3sin^{-1}x = sin^{-1}(3x – 4x³). x ∈ [-\(\frac { 1 }{ 2 }\), \(\frac { 1 }{ 2 }\)]

Solution:

Let θ = sin^{-1} ⇒ x = sin θ

∴ 3x – 4x³ = 3sinθ – 4sin³θ = sin3 θ

∴ 3θ = sin^{-1}(3x – 4x³)

⇒ 3sin^{-1}x = sin^{-1}(3x – 4x³)

Question 2.

3cos^{-1}x = cos^{-1}(4x³ – 3x). x ∈ [\(\frac { 1 }{ 2 }\), 1]

Solution:

Let θ cos^{-1} ⇒ x = cos θ

4x³ – 3x = 4cos³θ – 3cosθ = cos 3 θ

⇒ 3θ = cos^{-1}(4x³ – 3x)

⇒ 3cos^{-1}x = cos^{-1}(4x³ – 3x)

Question 3.

tan^{-1}\(\frac { 2 }{ 11 }\) + tan^{-1}\(\frac { 7 }{ 24 }\) = tan^{-1}\(\frac { 1 }{ 2 }\)

Solution:

Question 4.

2tan^{-1}\(\frac { 1 }{ 2 }\) + tan^{-1}\(\frac { 1 }{ 7 }\) = tan^{-1}\(\frac { 31 }{ 17 }\)

Solution:

Question 5.

tan^{-1}\(\frac{\sqrt{1+x^{2}}-1}{x}\), x ≠ 0

Solution:

Question 6.

tan^{-1}\(\frac{1}{\sqrt{x^{2}-1}}\), |x| > 1

Solution:

Question 7.

tan^{-1}\(\left(\sqrt{\frac{1-\cos x}{1+\cos x}}\right)\), x < π

Solution:

Question 8.

tan^{-1}\(\left(\frac{\cos x-\sin x}{\cos x+\sin x}\right)\), x < π

Solution:

Question 9.

tan^{-1}\(\frac{x}{\sqrt{a^{2}-x^{2}}}\), |x| < a

Solution:

Question 10.

tan^{-1}\(\left(\frac{3 a^{2} x-x^{3}}{a^{3}-3 a x^{2}}\right), a>0 ; \frac{-a}{\sqrt{3}} \leq x \leq \frac{a}{\sqrt{3}}\).

Solution:

Question 11.

tan^{-1}[2 cos(2 sin^{-1}\(\frac{1}{2}\))]

Solution:

Question 12.

cot(tan^{-1} a + cot^{-1} a)

Solution:

Since tan^{-1} a + cot^{-1} a = \(\frac{π}{2}\),

cot(tan^{-1} a + cot^{-1} a = cot(\(\frac{π}{2}\)) = 0

Question 13.

tan\(\frac{1}{2}\)[\(\left[\sin ^{-1} \frac{2 x}{1+x^{2}}+\cos ^{-1} \frac{1-y^{2}}{1+y^{2}}\right]\))], |x| < 1, y > 0 and xy < 1

Solution:

Question 14.

If sin(sin^{-1}\(\frac{1}{5}\) + cos^{-1}x) = 1, then find the value of x.

Solution:

Question 15.

If tan^{-1}\(\frac{x-1}{x-2}\) + tan^{-1}\(\frac{x+1}{x+2}\), then find the value of x.

Solution:

Question 16.

sin^{-1}\(\left(\sin \frac{2 \pi}{3}\right)\)

Solution:

Question 17.

tan^{-1}\(\left(\tan \frac{3 \pi}{4}\right)\)

Solution:

Question 18.

tan\(\left(\sin ^{-1} \frac{3}{5}+\cot ^{-1} \frac{3}{2}\right)\)

Solution:

Question 19.

cos^{-1}\(\left(\cos \frac{7 \pi}{6}\right)\) is equal to

a. \(\frac{7π}{6}\)

b. \(\frac{5π}{6}\)

c. \(\frac{π}{3}\)

d. \(\frac{π}{6}\)

Solution:

b. \(\frac{5π}{6}\)

Question 20.

sin\(\left(\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)\right)\) is equal to

a. \(\frac{1}{2}\)

b. \(\frac{1}{3}\)

c. \(\frac{1}{4}\)

d. 1

Solution:

d. 1

Question 21.

tan^{-1}\(\sqrt{3}\) – cot^{-1}\(\sqrt{3}\) is equal to

a. π

b. – \(\frac{π}{2}\)

c. 0

d. 2\(\sqrt{3}\)

Solution:

b. – \(\frac{π}{2}\)

tan^{-1}\(\sqrt{3}\) – cot^{-1}(-\(\sqrt{3}\))

= \(\sqrt{3}\) – (π – cot^{-1}\(\sqrt{3}\))

= (tan^{-1}\(\sqrt{3}\) + cot^{-1}\(\sqrt{3}\)) – π

= \(\frac{π}{2}\) – π = – \(\frac{π}{2}\)