Prove that:cos -1 (4x3 – 3x) = 3 cos -1 x, 1/2 ≤ x ≤ 1.

1.	Prove that:cos -1 (4x3 – 3x) = 3 cos -1 x, 1/2 ≤ x ≤ 1.
Answer» cos ^-1 (4x³ – 3x) = 3 cos ^-1 x, 1/2 ≤ x ≤ 1 Take x = cos θ Where θ = cos ^-1 x Here LHS = cos ^-1 (4x³ – 3x) By substituting the value of x = cos ^-1 (4 cos³θ – 3 cos θ) So we get = cos ^-1 (cos3θ) = 3θ By substituting the value of θ = 3 cos ^-1 x = RHS Hence, it is proved.

Answer»

cos ^-1 (4x³ – 3x) = 3 cos ^-1 x, 1/2 ≤ x ≤ 1

Take x = cos θ

Where θ = cos ^-1 x

Here LHS = cos ^-1 (4x³ – 3x)

By substituting the value of x

= cos ^-1 (4 cos³θ – 3 cos θ)

So we get

= cos ^-1 (cos3θ)

= 3θ

By substituting the value of θ

= 3 cos ^-1 x

= RHS

Hence, it is proved.

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