Put x = cos θ= sin–1(2tan–1)1 – cosθ = 2 sin2 and 1 + cos θ = 2 cos2= sin–1(2tan–1)= sin–1(2tan–1)= sin–1(2tan–1(tan))= sin–1()= sin–1(θ)But θ = cos–1x∴ The above expression becomes sin–1(cos–1x)

1 A 1 B 1 C 1 D 1 E 1 F 1 G 1 H 1 I 1 J 2 A 2 B 2 C 2 D 2 E 2 F 2 G 2 H 3 A 3 B 3 C 3 D 3 E 3 F 3 G 3 H 4 A 4 B 4 C 4 D 4 E 4 F 4 G 4 H 5 A 5 B 5 C 5 D 5 E 5 F 6 A 6 B 6 C 6 D 6 E 6 F 7 A 7 B 7 C 7 D 7 E 7 F 7 G 7 H 7 I 7 J

RD Sharma - Volume 1

4. Inverse Trigonometric Functions

Exercise 4.1

1 A 1 B 1 C 1 D 1 E 1 F 2 A 2 B 3 A 3 B 3 C 3 D 4 5

Exercise 4.2

1 2 3 4 A 4 B 4 C 4 D 5 A 5 B 5 C 5 D

Exercise 4.3

1 A 1 B 1 C 1 D 2 A 2 B 3 A 3 B 3 C

Exercise 4.4

1 A 1 B 1 C 1 D 2 A 2 B 3 A 3 B 1 A

Exercise 4.5

1 A 1 B 1 C 1 D 2 3 A 3 B 3 C 3 D

Exercise 4.6

1 A 1 B 1 C 1 D 2 3 A 3 B 3 C 3 D

Exercise 4.7

Exercise 4.8

1 A 1 B 1 C 1 D 1 E 1 F 1 G 1 H 1 I 2 A 2 B 2 C 2 D 3 4

Exercise 4.9

1 A 1 B 1 C 2 A 2 B 2 C 3

Exercise 4.10

1 A 1 B 1 C 1 D 1 E 2 3 4 5 6 7 8 9 10

Exercise 4.11

1 A 1 B 1 C 2 3 A 3 B 3 C 3 D 3 E 3 F 3 G 3 H 3 I 3 J 4

Exercise 4.12

1 2 A 2 B 2 C 3 A 3 B

Exercise 4.13

1 2 3 4

Exercise 4.14

1 A 1 B 1 C 1 D 2 A 2 B 2 C 2 D 2 E 2 F 2 G 2 H 2 I 2 J 3 4 A 4 B 5 6 7 A 7 B 8 A 8 B 8 C 8 D 8 E 8 F 9 10 11

MCQ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Very short answer

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Q. 7 J

Write each of the

Class 12th RD Sharma - Volume 1 4. Inverse Trigonometric Functions

Answer :

Put x = cos θ

= sin^–1(2tan^–1)

1 – cosθ = 2 sin² and 1 + cos θ = 2 cos²

= sin^–1(2tan^–1)

= sin^–1(2tan^–1(tan))

= sin^–1()

= sin^–1(θ)

But θ = cos^–1x

∴ The above expression becomes sin^–1(cos^–1x)

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