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underset(m =1)overset(n)sum tan^(-1) ((2...

`underset(m =1)overset(n)sum tan^(-1) ((2m)/(m^(4) + m^(2) + 2))` is equal to

A

` tan^(-1)(n^(2) +n) `

B

` "tan"^(-1)((n^(2)+n +1)/(n^(2) +n + 2))`

C

` "tan"^(-1)((n)/(n+1))`

D

` "tan"^(-1)((n^(2) +n)/(n^(2) + n + 2)) `

Text Solution

Verified by Experts

The correct Answer is:
D
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VMC MODULES ENGLISH-INVERSE TRIGONOMETRY-LEVEL-2
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  2. Range of the function f (x) = cos^-1 (-{x}), where {.} is fractional ...

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  3. underset(m =1)overset(n)sum tan^(-1) ((2m)/(m^(4) + m^(2) + 2)) is equ...

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  4. The number of real solutions (x, y), where |y| = sin x, y = cos^-1 (co...

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  5. If f(x)=cos^(- 1)x+cos^(- 1){x/2+1/2sqrt(3-3x^2)}then

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  6. Consider the system of equations cos^(-1)x + (sin^(-1) y)^(2) = (p pi^...

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  7. Let f(x) =e^(cos^(-1)sin(x+pi/3))then

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  8. If tan^-1 y=4 tan^-1x, then y is infinite if

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  9. The sum of the infinite terms of the series "tan"^(-1)((1)/(3))+ "tan...

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  10. If sin^-1x+sin^-1y+sin^-1z=(3pi)/2 and f(1)=2. f(p+q)=f(p). f(q)AAp,q...

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  11. If the mapping f(x) = mx + c, m gt 0 maps [-1,1] onto [0,2], then t...

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  12. Statement 1: tan^(-1)((3)/(4))+tan^(-1)((1)/(7))=(pi)/(4) Statement ...

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  13. Statement 1: The value of cot^(-1)((7)/(4))+cot^(-1)((19)/(4))+...+cot...

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  14. Statement 1: If x=(1)/(5 sqrt(2)), then [x cos(cot^(-1)x)+sin(cot^(-1)...

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  15. The number of the solutions of the equation 2 sin^(-1) sqrt(x^(2) + x ...

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  16. The sum of the series to infinity cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^...

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  17. If lim(n to oo) sum(k=2)^(n)cos^(-1)((1+sqrt((k-1)(k+2)(k+1)k))/(k(k+...

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  18. Number of solutions of the equation tan^(-1)((1)/(a-1))=tan^(-1)((1)/...

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  19. The sum of the infinite series cot^(-1)((7)/(4))+cot^(-1)((19)/(4))+co...

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  20. The set of values of 'a' for which x^(2) + ax + sin^(-1)(x^(2) -4x + 5...

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