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Find the sum of each of the following se...

Find the sum of each of the following series :(i) `tan^-1(1/(x^2+x+1))+tan^-1 (1/(x^2+3x+3))+tan^-1(1/(x^2+5X+7))+tan^-1(1/x^2+7x+13))`......upto n.

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The correct Answer is:
`arc tan (x+n)-arc tan x`
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MOTION-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise -3
  1. Solve the following inequality: arc cot^(2)x-5 at cotx+6gt0

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  2. Solve the following inequalities arc sin x gt arc cos x

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  3. Solve the following inequalities tan^(2) (arc sin x)gt 1

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  4. Solve the following system of inequations: 4(tan^(-1)x)^2-8tan^(-1)x+3...

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  5. Solve for x : sin^(- 1)(sin((2x^2+4)/(1+x^2)))lt pi-3

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

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

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  8. Find the sum of the series cot^(-1) 7+cot^(-1)13+cot^(-1)21+cot^(-1)...

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

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  10. Find the sum of the series tan^(-1) 1/2+tan^(-1) 1/8+tan^(-1) 1/18+t...

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  11. If the sum sum(n=1)^10 sum(m=1)^10 tan^(-1) (m/n) = k pi, find the va...

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  12. Find the value of tan { 1/2 sin^(-1) ((2x)/(1+x^(2))) + 1/2 cos^(-1...

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  13. 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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  14. Let y = sin^-1 (sin8) - tan^-1(tan 10) + cos^(-1) '(cos12)-sec^(-1) (...

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  15. Let u = cot^(-1) sqrt(cos 2 theta) - tan^(-1) sqrt( cos 2 theta) , ...

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  16. If x in [-1,-1/2] then express the function f(x)=sin^(-1) (3x-4x^(3))+...

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  17. Prove that tan[pi/4+1/2cos^(-1)""a/b]+tan[pi/4-1/2cos^(-1)""a/b]=2b/a

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  18. Q. prove that the equation ,(sin^-1)^3+(cos^-1)^3=alpha pi^3 has no ro...

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  19. Q.34 Q.34 Show that the roots r,s and t of the cubic Show that the roo...

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  20. Find the set of value of 'a' for which the equation 2 cos^(-1) x=a +a^...

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