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Write the tan^-1 (frac{3a^2 x-x^3}{a^3- ...

Write the `tan^-1 (frac{3a^2 x-x^3}{a^3- 3 ax^2)), a>0,- frac {a}{ 3} le x le frac{a}{ 3}`. in the simplest form.

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The correct Answer is:
`3tan^(-1)""(x)/(a)`
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BETTER CHOICE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE (MCQ)
  1. Solve: tan^-1 (x+3) + tan^-1 (x-3) = tan^-1 (frac{4}{39}), x>0

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  2. Solve: tan^-1 (x+4) + tan^-1 (x-4) = tan^-1 (frac{4}{67}), x>0

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

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

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  5. Prove that 2tan^(-1)""(1)/(5)+tan^(-1)""(1)/(4)=tan^(-1)""(32)/(43)

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  6. Prove that sin^(-1)""(3)/(5)+sin^(-1)""(8)/(17)=cos^(-1)""(36)/(85)

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  7. Prove that sin^(-1)""(4)/(5)+sin^(-1)""(5)/(13)=cos^(-1)""(16)/(65)

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  8. Prove that sin^(-1)(2x.sqrt(1-x^(2)))=2cos^(-1)x,(1)/(sqrt(2))lexlt1

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  9. Write tan^-1( sqrt (frac {1-cos x}{1+cos x})), x < pi in the simplest...

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  10. Prove that cot^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/...

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  11. Solve the Equation : tan^-1 ((x-1)/(x+2)) + tan^-1 ((2x-1)/(2x+1)) = t...

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  12. If sin(sin^(-1)""(1)/(5)+cos^(-1)x)=1, find the value of x.

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  13. Write tan^(-1)((1)/(sqrt(x^(2)-1))),|x|gt1 in simplest form.

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  14. Simplify tan^-1[(acosx-bsinx)/(bcosx+asinx)] if a/b tanx>-1

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  15. Write the tan^-1 (frac{3a^2 x-x^3}{a^3- 3 ax^2)), a>0,- frac {a}{ 3} l...

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

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

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

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

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

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