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Find the value of sum(r=0)^(oo) tan^(-1...

Find the value of `sum_(r=0)^(oo) tan^(-1) ((1)/(1 + r + r^(2)))`

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To find the value of the infinite series \[ \sum_{r=0}^{\infty} \tan^{-1} \left( \frac{1}{1 + r + r^2} \right), \] we can start by simplifying the term inside the summation. ...
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CENGAGE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-Illustration
  1. Solve tan^(-1) x + cot^(-1) (-|x|) = 2 tan^(-1) 6x

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  2. If a(1), a(2), a(3),...., a(n) is an A.P. with common difference d, th...

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  3. Find the value of sum(r=0)^(oo) tan^(-1) ((1)/(1 + r + r^(2)))

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  4. Find the sum sum(r =1)^(oo) tan^(-1) ((2(2r -1))/(4 + r^(2) (r^(2) -2r...

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  5. Find the value of 4 tan^(-1).(1)/(5) - tan^(-1).(1)/(70) + tan^(-1).(1...

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  6. If (x -1) (x^(2) + 1) gt 0, then find the value of sin((1)/(2) tan^(-1...

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  7. Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if ...

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  8. Prove that cot^(-1).(3)/(4) + sin^(-1).(5)/(13) = sin^(-1).(63)/(65)

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  9. Solve : sin^(-1)x + sin^(-1) 2x = (pi)/(3)

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  10. Solve sin^(-1) x + sin^(-1) (1 - x) = cos^(-1) x

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  11. Solve : cos^(-1)(1/2x^2+sqrt(1-x^2).sqrt(1-(x^2)/4))=cos^(-1)x/2-cos^(...

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  12. If x in (0, (pi)/(2)), then show that cos^(-1) ((7)/(2) (1 + cos 2 x) ...

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  13. Which of the following angles is greater ? theta(1) = sin^(-1).(4)/(...

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  14. Find the value lim(n rarr oo) sum(k=2)^(n) cos^(-1) ((1 + sqrt((k -...

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  15. If f(x) = sin^(-1) x then prove that lim(x rarr (1^(+))/(2)) f(3x -4x...

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

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  17. If A = 2 tan^(-1) ( 2 sqrt2 -1) " and " B = 3 sin ^(-1) ( 1/3) + sin^(...

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  18. If sin^(-1)(2x)/(1+x^2)=tan^(-1)(2x)/(1-x^2) , then find the value of ...

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  19. If sin^(-1)((4x)/(x^2+4))+2tan^(-1)(-x/2) is independent of x , find t...

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  20. If cos^(-1).(6x)/(1 + 9x^(2)) = -(pi)/(2) + 2 tan^(-1) 3x, then find t...

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