INVERSE TRIGONOMETRICFUNCTIONS | Class XII NCERT Solution | Chapter 2 | Miscellaneous Exercise
Channel: IMPETUS GURUKUL 
Date: 02/08/2021

INVERSE TRIGONOMETRICFUNCTIONS | Class XII NCERT Solution | Chapter 2 | Miscellaneous Exercise 
Miscellaneous Exercise on Chapter 2


Find the value of the following:
1. –1 13
cos cos
6
  π
    2. –1 7
tan tan
6
  π
   
Prove that
3. –1 –1 3 24 2sin tan
5 7
= 4. –1 –1 –1 8 3 77 sin sin tan
17 5 36
+ =
5. –1 –1 –1 4 12 33
cos cos cos
5 13 65
+ = 6. –1 –1 –1 12 3 56 cos sin sin
13 5 65
+ =
7. –1 –1 –1 63 5 3
tan sin cos
16 13 5
= +
8. –1 1 1 1 1 1 1 1
tan tan tan tan
5 7 3 8 4
− − − π
Prove that
9. –1 –1 1 1
tan cos
2 1
x
x
x
  −
=     +
, x ∈ [0, 1]
10. –1 1 sin 1 sin
cot
1 sin 1 sin 2
x x x
x x
  + + −  =
  + − −
, 0,
4
x
  π
∈   
11. –1 1 1 1 –1 tan cos
1 1 4 2
x x
x
x x
  + − − π   = −
  + + −
,
1
1
2
− ≤ ≤x [Hint: Put x = cos 2θ]
12. 9 9 1 9 2 2 1 1 sin sin
8 4 3 4 3
π − − − =
Solve the following equations:
13. 2tan–1 (cos x) = tan–1 (2 cosec x) 14. –1 –1 1 1 tan tan ,( 0)
1 2
x
x x
x
−
= 
+
15. sin (tan–1 x), | x|  1 is equal to
(A)
2
1
x
− x
(B)
2
1
1− x
(C)
2
1
1+ x
(D)
2
1
x
+ x
16. sin–1 (1 – x) – 2 sin–1 x =
2
π
, then x is equal to
(A) 0,
1
2
(B) 1,
1
2
(C) 0 (D)
1
2
17.
1 1 tan tan
x x y
y x y
− −   −
−     +
 is equal to
(A)
2
π
(B)
3
π
(C)
4
π
(D)
3
4
− π



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Today’s topic is : Inverse Trigonometric Functions Class XII Chapter 2 Ex 2.3