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Id a,b,c are distinct non-zero real numb...

Id `a,b,c` are distinct non-zero real numbers having the same sign. Prove that
`Cot^(-1)((ab+1)/(a-b)) +cot^(-1)((bc+1)/(b-c))+ Cot^(-1)((ca+1)/(c-a)) = pi (or) 2 pi`.

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The correct Answer is:
`pi` (or) `2pi`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-INVERSE TRIGONOMETRIC FUNCTIONS-TEXTUAL EXERCISES ( EXERCISE - 8(a) III).
  1. కింది వాటిని రుజువు చేయండి. 4 tan^-1 (1/5) + tan^-1 (1/99) - tan^-1 (1...

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  2. If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2)...

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  3. tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

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  4. Prove that sin[Cot^(-1) (2x)/(1-x^2)+Cos^(-1)((1-x^(2))/(1+x^(2)))]=1.

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  5. Prove that tan{(pi)/4 + 1/2 Cos^(-1)((a)/(b))}+tan{((pi)/4-1/2 Cos^(-1...

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  6. If Cos^(-1)p+Cos^(-1)q+Cos^(-1)r = pi then, P.T. p^(2)+q^(2)+r^(2) = 2...

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  7. If Sin^(-1)(2p)/(1+p^(2)) - Cos^(-1)((1-q^(2))/(1+q^(2))) = Tan^(-1) (...

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  8. Id a,b,c are distinct non-zero real numbers having the same sign. Prov...

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  9. If Sin^(-1)(x)+Sin^(-1)(y)+Sin^(-1)(z) = pi, prove that xsqrt(1-x^(2))...

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  10. If Tan^(-1) x + Tan^(-1) y + Tan^(-1) z = pi then prove that x+y+z = x...

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  11. If Tan^(-1)x+Tan^(-1)y + Tan^(-1)z = (pi)/2, then prove that xy + yz +...

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  12. If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=(pi)/4 then x=

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  13. The arithmetic mean of the non-zero solutions of the equation "Tan"^...

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  14. Solve 3Sin^(-1)((2x)/(1+x^(2))) - 4 Cos^(-1)((1-x^(2))/(1+x^(2)))+2Tan...

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  15. Solve the following equations : sin^(-1)(1-x)-2sin^(-1)x=(pi)/2 the...

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  16. solve the following equations Cot^(-1)((1+x)/(1-x))=1/2Cot^(-1)(1/x)...

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  17. Solve the following equations. (ii) tan [ chi o sigma^(-1) (1)/( xi)...

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  18. Solve the following equations. cos^(-1) x + sin^(-1) "" (x)/(2) = (...

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  19. solve the following equations Cos^(-1) (sqrt(3).x)+Cos^(-1)(x)=(pi)/...

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  20. Solve the following equations. sin [ sin^(-1) ((1)/(5)) + cos^(-1) x...

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