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Find the value of sum(r = 1)^(10) sum(s ...

Find the value of `sum_(r = 1)^(10) sum_(s = 1)^(10) tan^(-1) ((r)/(s))`

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To find the value of the expression \[ \sum_{r=1}^{10} \sum_{s=1}^{10} \tan^{-1}\left(\frac{r}{s}\right), \] we can follow these steps: ...
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CENGAGE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-Illustration
  1. Prove that tan^(-1) x + tan^(-1).(1)/(x) = {(pi//2,"if" x gt 0),(-pi//...

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  2. For which values of x, function f(x) = sin^(-1) x + sin^(-1).(1)/(x) +...

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  3. Find the value of sum(r = 1)^(10) sum(s = 1)^(10) tan^(-1) ((r)/(s))

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  4. If sin^(-1)xi in [0,1]AAi=1,2,3, .28 then find the maximum value of s...

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  5. If two angles of a triangle are tan^(-1) (2) and tan^(-1) (3), then fi...

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  6. Prove that cos^(-1).(4).(5) + cos^(-1).(12)/(13) = cos^(-1).(33)/(65)

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  7. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={ when ...

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  8. Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt...

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  9. Simplify [(3 sin 2 alpha)/(5 + 3 cos 2 alpha)] + tan^(-1) [(tan alph...

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

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  11. Solve tan^(-1) x + sin^(-1) x = tan^(-1) 2x

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  12. Solve cot^(-1) ((3x^(2) + 1)/(x)) = cot^(-1) ((1 - 3x^(2))/(x)) - tan^...

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  13. If x gt y gt z gt 0, then find the value of "cot"^(-1) (xy + 1)/(x - y...

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  14. Solve tan^(-1) x + cot^(-1) (-|x|) = 2 tan^(-1) 6x

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

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

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

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

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

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

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