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

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-1x = 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-1x = sin-1(3x – 4x³)

Question 2.
3cos-1x = 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-1x = 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-1x) = 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 = – $$\frac{π}{2}$$