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Prove the following: 3cos−1x = cos−1(4x3 − 3x), x∈[1/2,1] - Mathematics

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Question

Prove the following: 

3cos−1x = cos−1(4x3 − 3x), `x ∈ [1/2, 1]`

Theorem
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Solution

Let x = cos θ

Then, cos−1x =  θ

We have,

R.H.S = cos−1(4x3 − 3x)

⇒ cos−1(4 cos3θ − 3 cos θ)

⇒ cos−1(cos 3θ) = cos−1(4x3 − 3x)

⇒ 3θ =  cos−1(4x3 − 3x)

⇒ 3 cos−1x = cos−1(4x3 − 3x)

R.H.S = L.H.S

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Chapter 2: Inverse Trigonometric Functions - Exercise 2.2 [Page 47]

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NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 2 Inverse Trigonometric Functions
Exercise 2.2 | Q 2 | Page 47

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