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Prove each of the following tan^(-1) x...

Prove each of the following
`tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x)/(sqrt(1+x^(2))`
`=-cos^(-1) (1)/(sqrt(1+x^(2))" when "x lt 0`

Answer

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Prove each of the following relation: cos^(-1)x=sec^(-1)1/x=pi-sin^(-1)sqrt(1-x^(2))=pi+"tan"^(-1)(sqrt(1-x^(2)))/x="cot"^(-1)x/(sqrt(1-x^(2))) when -1ltxlt0

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Knowledge Check

  • int(tan(cos^(-1)x)+cot(sin^(-1)x))/(sqrt(1-x^(2)))dx=

    A
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    B
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    D
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