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प्रश्न
Solve for x,
`2 tan^(−1) x + sin^(−1)((2x)/(1 + x^2)) = 4sqrt3`
बेरीज
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उत्तर
Given: `2 tan^(−1) x + sin^(−1)((2x)/(1 + x^2)) = 4sqrt3`
Put x = tan 0 ⇒ θ = tan−1 x
`2 tan^(-1) (tan θ) + sin^(-1) ((2tan θ)/(1 + tan^2 θ))`
= `4sqrt3`
`2θ + sin^(-1)(sin 2θ) = 4sqrt3`
`2θ + 2θ = 4sqrt3`
`4θ = 4sqrt3`
`θ = (4sqrt3)/4`
`∴ θ = sqrt3`
Now, `x = tan^(-1)x sqrt3 ...(∵ θ = tan^(-1))`
There is no solution for x.
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