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