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If "Tan"^(-1)1/(1+2)+"Tan"^(-1)1/(1+(2)(...

If `"Tan"^(-1)1/(1+2)+"Tan"^(-1)1/(1+(2)(3))+"Tan"^(-1)1/(1+(3)(4))+..."Tan"^(-1)1/(1+n(n+1))=Tan^(-1)theta`, then `theta` =

A

`n/(n+1)`

B

`(n+1)/(n+2)`

C

`n/(n+2)`

D

`(n-1)/(n+2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 1
  1. "Tan"^(-1)(yz)/(xsqrt(x^(2)+y^(2)+z^(2)))+"Tan"^(-1)(zx)/(ysqrt(x^(2)+...

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  2. "Tan"^(-1)(c(1)x-y)/(c(1)y+x)+"Tan"^(-1)(c(2)-c(1))/(1+c(2)c(1))+"Tan"...

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  3. If "Tan"^(-1)1/(1+2)+"Tan"^(-1)1/(1+(2)(3))+"Tan"^(-1)1/(1+(3)(4))+......

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

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  5. If x^(2)+y^(2)+z^(2)=r^(2), then Tan^(-1)((xy)/(zr))+Tan^(-1)((yz)/(xr...

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  6. If u=tan^(-1)(1/(sqrt(cos 2 theta)))-tan^(-1)(sqrt(cos 2 theta)), then...

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  7. If 0lexle1/2, then Sin^(-1)x+Sin^(-1)(x/2-sqrt(3-3x^(2))/2)=

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  8. If 1/2lexle1 then Cos^(-1)x+Cos^(-1)(x/2-sqrt(3-3x^(2))/2)=

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  9. If y is infinite and tan^(-1)y=4tan^(-1)x then

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  10. If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi then x+y+z=

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  11. If Tan^(-1)x+Tan^(-1)y+Tan^(-1)z=pi//2 then 1 - xy - yz - zx =

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  12. If Cos^(-1)x+Cos^(-1)y+Cos^(-1)z=pi,"then "x^(2)+y^(2)+z^(2)+2xyz=

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  13. If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=pi//2,"then "x^(2)+y^(2)+z^(2)+2xyz=

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  14. If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=pi then prove that n xsqrt(1-x^(2))+y...

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  15. If Sec^(-1)sqrt(1-x^(2))+Cosec^(-1)(sqrt(1+y^(2)))/y+"Cot"^(-1)1/z=3pi...

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  16. If Cos^(-1)(x/a)+Cos^(-1)(y/b)=theta,"then "x^(2)/a^(2)-(2xy)/(ab)cost...

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  17. If Cos^(-1)(x//2)+Cos^(-1)(y//3)=theta" then "9x^(2)-12xycostheta+4y^(...

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  18. If Sin^(-1)x+Sin^(-1)y=2pi//3,"then "Cos^(-1)x+Cos^(-1)y=

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  19. If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=(3pi)/2, then the value of x^(100)+y^...

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  20. If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2)...

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