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If tan ^(-1) ((1-x)/(1+x))= (1)/(2) tan^...

If `tan ^(-1) ((1-x)/(1+x))= (1)/(2) tan^(-1) x, x gt 0`, then x = ?

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The correct Answer is:
`1/(sqrt(3))`
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MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-EXERCISE 2 (b) (Short Answer Type Questions)
  1. Solve the following equations : tan^(-1) (x+1) +tan^(-1) (x-1) = ...

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  2. Solve the following equations : tan^(-1) (x+2) +tan^(-1) (x-2) = ...

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  3. If tan ^(-1) ((1-x)/(1+x))= (1)/(2) tan^(-1) x, x gt 0, then x = ?

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  4. Solve the following equations : tan^(-1). (2x)/(1-x^(2)) +cos^(-1)....

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  5. Solve the following equations : cos (tan^(-1) x ) = sin (cot^(-1)...

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  6. If sin(cot^(-1)(x+1))=costan^(-1)x, then x=

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  7. Solve the following equations : 2tan^(-1) (sin x) = tan^(-1) (2se...

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  8. Solve the following equations : cos (sin^(-1) x) = 1/2

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  9. Solve the following equations : tan^(-1) ((x-2)/(x-4)) +tan^(-1) (...

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  10. Solve for x , tan^(-1) ( x + 1) + tan^(-1) x + tan^(-1) ( x - 1) = t...

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  11. Solve for x : 3 sin^(-1) ((2x)/(1+x^(2))) - 4 cos^(-1) ((1-x^(2))...

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  12. Express each of the following in the simplest form: tan^(-1){(cosx)...

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  13. Write the following function in the simplest form: tan^(-1)((cosx-sinx...

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  14. Write the following function in the simplest form: tan^(-1)((cosx-sinx...

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  15. Write the following functions in the simplest form: tan^(-1){x/(a^2-x...

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  16. Write the following function in the simplest form: tan^(-1)(sqrt(1+x^2...

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  17. Write the following in the simplest form : tan ^(-1) ((sqrt(1-x^(...

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  18. Prove that : tan^(-1) ((sqrt(1-x^(2)))/(1+x)) = 1/2 cos^(-1) x

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  19. prove that 1/2tan^-1x=cos^-1xsqrt((1+sqrt(1+x^2))/(2sqrt(1+x^2))

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  20. Prove that : tan^(-1) [ (sqrt(1+z) +sqrt(1-z))/(sqrt(1+z) -sqrt(1-z...

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