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Prove that : cot^(-1)((1+ab)/(a-b))+cot^...

Prove that : `cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1+ca)/(c-a))=pi,(a>b>c>0)`

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. the value of 3tan^- 1(1/4)+tan^- 1(1/20)+tan^- 1(1/1985)

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  2. If sin^2x + sin^2y < 1 ; x, y in R then prove that sin^-1(tanx . tany...

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  3. Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1...

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  4. Let cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)b epidot If x satisfies the e...

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  5. If alpha=2 arc t a n((1+x)/(1-x)) in B=a r c s i n((1-x^2)/(1+x^2))...

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  6. solve:sin^-1x+sin^-1 2x=pi/3

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  7. Arithmetic mean of the non-zero solutions of the equation tan^-1 (1/(2...

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  8. Solve : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x

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  9. Solve sin^(-1)x-cos^(-1)x=sin^(-1)(3x-2)

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  10. Solve the following equation: sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

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  11. If tan^(- 1)((2x)/(x^2-1))+cos^(- 1)(x^2-1)/(x^2+1)=(2pi)/3 then x=

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  12. Find the sum of the series :(tan^- 1)1/3+(tan^- 1)2/9+....+(tan^- 1)(2...

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  13. Find the sum to n terms cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+ cot^(-1)...

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  14. Find the sum of each of the following series :(i) tan^-1(1/(x^2+x+1))+...

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  15. Find the domain of definition the following function: f(x)=log(10)(1-l...

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  16. f(x)=sqrt(sin(cosx))+ln(-2cos^2x+3cosx+1)+e^(cos^- 1)((2sinx+1)/(2sqrt...

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  17. Prove that the identities, sin^-1 cos(sin^-1x)+cos^-1 sin(cos^-1x)=pi...

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  18. Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=[pi/4m/n gt;-1(-3pi)/4m...

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  19. The sum of the infinte series sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(2)-1)...

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  20. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, show that x^4+y^4+z^4+4x^2y^2z^2=...

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