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The value of Sigma(n=1)^(3) tan^(-1)(1/...

The value of `Sigma_(n=1)^(3) tan^(-1)(1/n)` is

A

0

B

`pi`

C

`pi//2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`underset(n=1)overset(3)Sigma tan^(-1)(1)/(n)=tan^(-1)+tan^(-1)1/2+tan^(-1)1/3`
`rarr underset(n=1)overset(3)Sigma tan^(-1)(1)/(n)=(pi)/(4)O+tan^(-1)((1/2+1/3)/(1-1/2xx1/3))`
`rarrunderset(n=1)overset(3)Sigma tan^(-1)(1)/(n)=(pi)/(4)+tan^(-1)1=(pi)/(4)+(pi)/(4)=(pi)/(2)`
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Chapter Test
  1. The value of Sigma(n=1)^(3) tan^(-1)(1/n) is

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  2. If sin^(-1)(1-x) -2sin^(-1)x=(pi)/(2) then x equal

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  3. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

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  4. If tan theta + tan((pi)/(3)+theta) + tan((-pi)/(3)+theta) = ktan 3 the...

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  5. If 1/2 le x le 1 then sin^(-1) (3x-4x^(3)) equals

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  6. The value of tan (2 "tan"^(-1)(1)/(5)-(pi)/(4)) is

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  7. If tan(x+y)=33, and x= tan^(-1)3, then: y=

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  8. Two angles of a triangle are cot^-1 2 and cot^-1 3, then the third ang...

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  9. If A=2tan^(-1)(2sqrt(2)-1)a n dB=3sin^(-1)(1/3)+sin^(-1)(3/5), then wh...

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

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  11. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2) the value of x^(100)+y^(10...

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  12. The value of (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec...

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  13. If a,b are positive quantitis and if a(1)=(a+b)/(2), b(1)=sqrt(a(1)b) ...

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  14. tan""(2pi)/(5)-tan""(pi)/(15)-sqrt3tan""(2pi)/(5)tan""(pi)/(15) is equ...

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  15. If a(1),a(2),a(3),….a(n) is a.p with common difference d then tan{tan...

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  16. If x=sin(2tan^(- 1)2), y=sin(1/2tan^(- 1)(4/3)) , then -

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  17. Which of the following angles is greater? theta1=sin^(-1)(4/5)+sin^(-...

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  18. The value of cos[1/2 cos^(-1){cos(sin^(-1)((sqrt63)/(8)))}] is

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  19. Solve tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1)"\ "8/(31)

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  20. If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)...

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  21. The sum of the two angles cot^(-1) 3 and cosec^(-1) sqrt(5) is

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