RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12th

Q. No. 4 of MCQ

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4

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If , then


We are given that,


We need to find the value of



By property of inverse trigonometry,


cos-1 a + cos-1 b = cos-1(ab - √(1 – a2)√(1 – b2))


So,




Simplifying further,



Taking cosine on both sides,



Using the property of inverse trigonometric function,


cos(cos-1 x) = x




To simplify it further, take square on both sides.



Using algebraic identity,


(x – y)2 = x2 + y2 – 2xy



Simplifying it further,



Shifting all terms at one side,



Using trigonometric identity,


sin2 x + cos2 x = 1


⇒ sin2 x = 1 – cos2 x


We get,


1

Chapter Exercises

Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise 4.4
Exercise 4.5
Exercise 4.6
Exercise 4.7
Exercise 4.8
Exercise 4.9
Exercise 4.10
Exercise 4.11
Exercise 4.12
Exercise 4.13
Exercise 4.14
Very short answer
MCQ

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14

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20

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21

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26

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27

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28

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29

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30

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31

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32

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