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If x, y, z are natural numbers such that...

If x, y, z are natural numbers such that `cot^(-1)x+cot^(-1)y=cot^(-1)z` then the number of ordered triplets (x, y, z) that satisfy the equation is

A

0

B

1

C

2

D

infinite solutions

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The correct Answer is:
D
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AAKASH SERIES-INVERSE TRIGNOMETRIC FUNCTIONS-LECTURE SHEET (EXERCISE - III) (STRAIGHT OBJECTIVE TYPE QUESTIONS)
  1. Find the values of cos(2cos^(-1)x+sin^(-1)x) at x = 1/5, where 0 le co...

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  2. The value of x for which sin[cot^(-1)(1+x)]=cos(tan^(-1)x) is :

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  3. The solutio set of the equation sin^(-1)sqrt(1-x^(2))+cos^(-1)x="cot"^...

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  4. The sum of the solutions of the equation 2sin^(-1)sqrt(x^(2)+x+1)+cos^...

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  5. The number of real solutions of Tan^(-1)(sqrt(x(x+1))+sin^(-1)sqrt(x^(...

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  6. If tan^(-1)(sin^(2)theta-2sintheta+3)+cot^(-1)(5^(sec^(2)beta)+1)=pi/2...

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  7. The number of integral values of k for which the equation sin^(-1)x+ta...

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  8. The number of solutions for the equation cos^(-1)(1-x)+mcos^(-1)x=(npi...

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  9. The number of solutions of the equation 3Cos^(-1)x-pix-pi/2=0

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  10. The number of real solutions of abs(y)=sinx, y=cos^(-1)(cosx), -2pi le...

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  11. Number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)Sin^(-1)...

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  12. The solution of the inequality log(1//2)sin^(-1)x gt log(1//2)cos^(-1)...

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  13. If cot^(-1)""n/pi gt pi/6, n in N, then the maximum value of n is

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  14. If (cot^(-1)x)^(2)-7(cot^(-1)x)+10 gt 0, then x lies in the interval

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  15. If [Cot^(-1)x]+[Cos^(-1)x]=0 where x is non-negative real number and [...

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  16. The complete solution set of [tan^(-1)x]^(2)-8[tan^(-1)x]+16 le 0, whe...

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  17. The value of x for which Cos^(-1)(cos4) gt 3x^(2)-4x is

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  18. The least integral value of k for which (k-2)x^(2)+8x+k+4 gt Sin^(-1)(...

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  19. If x, y, z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1)z...

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  20. Which of the following function(s) is/are periodic?

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