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Prove that tan^(-1)x+tan^(-1)(2x)/(1-x^2...

Prove that `tan^(-1)x+tan^(-1)(2x)/(1-x^2)=tan^(-1)((3x-x^3)/(1-3x^2)),|x|<1/(sqrt(3))`

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OSWAAL PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-SHORT ANSWER TYPE QUESTIONS - II
  1. Solve : tan^(-1)(x-1)/(x-2)+tan^(-1)(x+1)/(x+2)=pi/4

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  2. Prove that: 3cos^(-1)x=cos^(-1)(4x^3-3x), x in [1/2,1]

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  3. Prove that tan^(-1)x+tan^(-1)(2x)/(1-x^2)=tan^(-1)((3x-x^3)/(1-3x^2)),...

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  4. tan^(-1)x+tan^(-1)y=pi+tan^(-1)((x+y)/(1-xy))

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  5. Prove that: 2tan^(-1)1/2+tan^(-1)1/7=tan^(-1)(31)/(17)

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  6. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

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  7. Solve the equation sin^(-1)y x+sin^(-1)6sqrt(3)x=(-pi)/2dot

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  8. cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=(x)/...

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

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

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

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

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

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

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

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

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

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

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

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

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