Prove that :
$3 c o s^{- 1} x = c o s^{- 1} (4 x^{3} - 3 x)$

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Solution

Let $x = cos θ$
$c o s^{- 1} x = θ$
RHS :
$c o s^{- 1} (4 x^{3} - 3 x)$
$= c o s^{- 1} (4 {cos}^{3} θ - 3 cos θ)$
$= c o s^{- 1} (c o s 3 θ)$
$= 3 θ$
$= 3 c o s^{- 1} x$
=LHS

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Similar questions

3 {cos}^{- 1} x = {cos}^{- 1} (4 x^{3} - 3 x), x ϵ [\begin{matrix} \frac{1}{2}, 1 \end{matrix}]

3 {cos}^{- 1} x = {cos}^{- 1} ({4 x}^{3} - 3 x), x \in [\frac{1}{2}, 1]

Prove the following,

$3 c o s^{- 1} x = c o s^{- 1} (4 x^{3} - 3 x), x ϵ [\frac{1}{2}, 1]$ .

3 {cos}^{- 1} x = {cos}^{- 1} (4 x^{3} - 3 x) x \in [1 / 2, 1]

{cos}^{- 1} (4 x^{3} - 3 x) = 2 π - 3 {cos}^{- 1} x

x

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