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If x + y + z = xyz and x, y, z gt 0, the...

If `x + y + z = xyz and x, y, z gt 0`, then find the value of `tan^(-1) x + tan^(-1) y + tan^(-1) z`

A

0

B

`pi//2`

C

1

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Exercise
  1. A solution of the equation tan^(-1)(1+x)+tan^(-1)(1-x)=(pi)/(2) is

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  2. If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+...

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  3. If x + y + z = xyz and x, y, z gt 0, then find the value of tan^(-1) x...

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  4. If xy +yz+zx=1 then tan^(-1)x+tan^(-1)y+tan^(-1)z=

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  5. If x1,x2, x3, x4 are the roots of the equation x^4-x^3 sin2 beta+ x^2....

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  6. The value of cos (2Cos^-1 0.8) is

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  7. If 0 le x le 1 then cos^(-1)(2x^(2)-1) equals

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  8. The value of tan[cos^(-1)(4/5)+tan^(-1)(2/3)] is 6/(17) (b) 7/(16) (...

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  10. If sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2b)/(1+b^2)) = 2 tan^(-1)x then...

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  11. The value of cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx) -sqr...

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  12. The value of sin[cot^(-1){cos(tan^(-1) x)}] is

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  13. If x >1 , then 2\ tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is equal to 4tan^(-...

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  14. If A=tan^-1((xsqrt3)/(2k-x)) and B=tan^-1((2x-k)/(ksqrt3)) then find t...

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  15. If sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x then x equals

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  16. If -1 le x le 0 then cos^(-1)(2x^(2)-1) equals

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  17. If -1/2 le x le 1/2 hence sin^(-1)(3x-4x^(3)) equals

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  18. The value of sin^(-1)(sin 10) is

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  19. The value of tan^(-1)1+tan^(-1)2+tan^(-1)3 is

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  20. The value of sin^(-1)[cos((33pi)/5)] is

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