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Sum the following series to infinity :...

Sum the following series to infinity : `tan^(-1)(1/(1+1+1^2))+tan^(-1)(1/(1+2+2^2))+tan^(-1)(1/(1+3+3^2))+.................`

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  10. Prove that: sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi

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  11. Prove: tan^(-1)(1/4)+tan^(-1)(2/9)=sin^(-1)(1/(sqrt(5)))

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  12. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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  13. Solve for x: tan^(-1)3x+tan^(-1)2x=pi/4

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  14. Solve for x: tan^-1(x+1)+tan^-1(x-1)=tan^-1(8/31)

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

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  16. Solve for x :tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,x >0

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  17. Solve for x : cot^(-1)x-cot^(-1)(x+2)=pi/(12) , where x >0

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  18. Solve for x : tan^(-1)(x+2)+tan^(-1)(x-2)=tan^(-1)(8/(79)) , x >0

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  19. Solve for x : tan^(-1)(x/2)+tan^(-1)(x/3)=pi/4 , 0

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  20. Solve for x : tan^(-1)((x-2)/(x-1))+tan^(-1)((x+2)/(x+1))=pi/4

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