RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12th

Q. No. 4 A of Exercise 4C

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4 A

Prove that:


To Prove: cos-1 (1 – 2x2) = 2 sin-1 x


Formula Used: cos 2A = 1 – 2 sin2 A


Proof:


LHS = cos-1 (1 – 2x2) … (1)


Let x = sin A … (2)


Substituting (2) in (1),


LHS = cos-1 (1 – 2 sin2 A)


= cos-1 (cos 2A)


= 2A


From (2), A = sin-1 x,


2A = 2 sin-1 x


= RHS


Therefore, LHS = RHS


Hence proved.


Chapter Exercises

Exercise 4A
Exercise 4B
Exercise 4C
Exercise 4D
Objective Questions

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