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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 cos3 θ – 3 cos θ)
= cos–1(cos 3θ)
= 3θ
= 3cos–1x
= L.H.S.
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