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Solve for "x\ ":tan^(-1)(1-"x")/(1+"x")=...

Solve for `"x\ ":tan^(-1)(1-"x")/(1+"x")=1/2"tan"^(-1)"\ x";"x">0`

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The correct Answer is:
`(1)/(sqrt3)`
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OSWAAL PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-SHORT ANSWER TYPE QUESTIONS - II
  1. Solve for x : tan^(-1)x+2cot^(-1)x=(2pi)/3

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  2. Prove that s in^(-1)(8/(17))+sin^(-1)(3/5)=cos^(-1)((36)/(85))

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  3. Solve for "x\ ":tan^(-1)(1-"x")/(1+"x")=1/2"tan"^(-1)"\ x";"x">0

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  4. Prove that 2tan^(-1)(1/5)+sec^(-1)((5sqrt(2))/7)+2tan^(-1)(1/8)=pi/4...

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  5. Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+)x+sqrt(1-x))]=pi/4...

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  6. If tan^(-1)((x-2)/(x-4))+tan^(-1)((x+2)/(x+4))=pi/4, find the value of...

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  7. Solve for x : cos(tan^(-1)x)=sin(cot^(-1)3/4)

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  8. Prove the following: cos^(-1)((12)/(13))+sin^(-1)(3/5)=sin^(-1)((56)/...

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  9. Find the value of the following: tan1/2[sin^(-1)(2x)/(1+x^2)+cos^(-1)...

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  10. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

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  11. Show that: tan(1/2sin^(-1)3/4)=(4\ sqrt(-7))/3

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  12. Solve for x: tan^(-1)3x+tan^(-1)2x=pi/4

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  13. tan^(-1)((3)/(4))+tan^(-1)((3)/(5))-tan^(-1)((8)/(19))=

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  14. Prove that t a n^(-1)((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)

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  15. cos(sin^-1 (3/5)+ cot^-1(3/2)) = 6/(5sqrt13)

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  16. cos^(-1)((4)/(5))+cos^(-1)((12)/(13))=

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  17. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

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  18. Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^21)/(x^2+2)) ...

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  19. Prove that : 2tan^(-1)((3)/(4))-tan^(-1)((17)/(31))=(pi)/(4).

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  20. Solve for x : tan^(-1)((2x)/(1-x^2))+cot^(-1)((1-x^2)/(2x))=pi/3,-1ltx...

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