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प्रश्न
Prove the following:
`3cos^(-1) x = cos^(-1)(4x^3 - 3x), x in [1/2, 1]`
उत्तर १
To prove: `3cos^(-1) x = cos^(-1) (4x^3 - 3x), x in [1/2, 1]`
उत्तर २
To prove `3cos^(-1) x = cos^(-1) (4x^3 - 3x), x in [1/2, 1]`
Let x = cosθ. Then, cos−1 x = θ.
We have,
R.H.S = `cos^(-1)(4x^3 - 3x)`
`= cos^(-1)(4cos^3 theta- 3cos theta)`
`= cos^(-1)(cos 3theta) = cos^(-1)(4x^3 - 3x)`
`= 3theta = cos^(-1)(4x^3 - 3x)`
`= 3cos^(-1) x = cos^(-1)(4x^3 - 3x)`
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