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Write tan^(-1)((sqrt(1+x^(2))-1)/(x)),xn...

Write `tan^(-1)((sqrt(1+x^(2))-1)/(x)),xne0` simplest form.

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The correct Answer is:
`1/(2)"tan"^(-1)x`
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OMEGA PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Important Questions from Miscellaneous Exercise
  1. Prove that : cos^-1 (4/5) + cos^-1(12/13) = cos^-1 (33/65)

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  2. Write tan^(-1)((x)/(sqrt(a^(2)-x^(2)))) in simplest form.

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  3. Write tan^(-1)((sqrt(1+x^(2))-1)/(x)),xne0 simplest form.

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  4. Find the value of cos^(-1)(cos""(13pi)/(6))

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  5. What is the principal value of "cos"^(-1)("cos"(2pi)/(3))+"sin"^(-1)("...

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  6. Prove that cos^(-1)""(12)/(13)+sin^(-1)""(3)/(5)=sin^(-1)""(56)/(65)

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  7. Prove that tan^(-1)""(1)/(2)+tan^(-1)""(2)/(11)=tan^(-1)""(3)/(4)

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  8. Prove that tan^(-1)""(2)/(11)+tan^(-1)""(7)/(24)=tan^(-1)""(1)/(2).

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  9. Express tan^(-1)((cosx)/(1-sinx)),-(pi)/(2)ltxlt(pi)/(2) in the simple...

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  10. Prove that tan^(-1) (1/5)+ tan^(-1) (1/7) + tan^(-1) (1/3) + tan^(-1) ...

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  11. Show that sin^(-1)""(3)/(5)-sin^(-1)""(8)/(17)=cos^(-1)""(84)/(85)

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  12. Prove that : cot^-1[(sqrt(1+sin x) + sqrt(1-sin x))/(sqrt1+sin x + sqr...

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  13. Prove that (9pi)/(8)-9/(4)"sin"^(-1)1/(3)=9/(4)"sin"^(-1)(2sqrt(2))/(3...

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  14. Solve tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)""(8)/(31)

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  15. Prove that "tan"^(-1)sqrt(x)=1/(2)"cos"^(-1)((1-x)/(1+x)),x in[0,1].

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  16. Solve the 2 tan^-1 (cos x) = tan^-1 (2 cosec x).

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

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  18. Show that "sin"^(-1)(5/(13))+"cos"^(-1)(3/(5))="tan"^(-1)(63/(16)).

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  19. Prove that : "tan"^(-1)(x/(4)+1/(2)"cos"^(-1)a/(b))+"tan"(pi/(4)-1/(2)...

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  20. Prove that : "sin"^(-1)(2xsqrt(1-x^(2)))=2"cos"^(-1)x,1/(sqrt(2))lexle...

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