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Sum the following series to infinity: ta...

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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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Evaluate: tan^(-1)(1)+tan^(-1)(0),

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  2. Prove that: sum(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2...

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

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  4. Solve the equation: tan^-1(2x)+tan^-1 {(3x)} =pi/4

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  5. If a1,a2,a3, an are in arithmetic progression with common difference d...

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  6. Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x...

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  7. If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)...

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  8. Find the maximum and minimum values of (sin^(-1)x)^3+(cos^(-1)x)^3, wh...

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  9. the greatest and least values of (sin^(-1) x)^2+(cos^(-1)x)^2

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  10. Solve : 4sin^(-1)x=pi-cos^(-1)x

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  11. If (sin^(-1)x)^2+(cos^(-1)x)^2=(17pi^2)/(36) , find xdot

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  12. Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

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  13. Prove that : tan^(-1)(2/11)+tan^(-1)(7/24)=tan^(-1)(1/2)

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

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  15. Prove that: tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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  16. Prove that: tan^(-1)(1/7)+tan^(-1)(1/(13))=tan^(-1)(2/9) tan^(-1)(1...

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  17. If tan^(-1)2+tan^(-1)3+theta=pi, find the value of thetadot

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  18. What is greater, tan1 or tan^(-1)1?

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  19. Find the minimum value of n for which tan^(-1)(n/pi)>pi/4,n in Ndo...

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  20. Find the principal values of sec^(-1)(2/(sqrt(3))) and sec^(-1)(-2)

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