Question

Question 2: Prove 3cos¯¹ x = cos¯¹ (4x³ – 3x), x ∈ [1/2,1]

Class 12 - Math - Inverse Trigonometric Functions

Answer 1

i hope this is helpful

Answer 2

To prove: 3−1 = -¹ (4 ³ − 3), ∈ [ 1 /2 , 1].
Let cos-¹x = θ, then x = cos θ.
We have,

RHS
cos-¹ (4x ³-3x) = cos-¹(4cos³θ-3cosθ)
= cos-¹(cos 3θ) = 3θ = 3cos-¹x
= LHS