Question

simplify cos-1 (3x - 4x3)​

Answer 1

Step-by-step explanation:

We have to prove that 3cos

−1

x=cos

−1

(4x

3

−3x)

First consider RHS, cos

−1

(4x

3

−3x)

Let us take x=cosθ, we know that cos(3θ)=4cos

3

θ−3cosθ

⟹cos

−1

(4x

3

−3x)=cos

−1

(4cos

3

θ−3cosθ)=cos

−1

(cos(3θ))=3θ

∵θ=cos

−1

x, ⟹cos

−1

(4x

3

−3x)=3cos

−1

x

∴LHS=RHS

0≤3cos

−1

x≤π

0≤cos

1

x≤π/3

∴xϵ[

2

1

,1]

Hence proved.