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Prove that 3 tan^(-1) x= {(tan^(-1) ((...

Prove that
`3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}`

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AAKASH INSTITUTE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-TRY YOURSELF
  1. Find the principal value of cos^(-1)(1/2).

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  2. Find the principal value of each of the following: (i) tan^(-1)(1/(s...

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  3. The Principle value of cot ^(-1) (-sqrt3) is

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  4. Find the principal values of sec^(-1)(2/(sqrt(3))) and sec^(-1)(-2)

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  5. Find the principal value of cosec^(-1)(-2/sqrt3).

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  6. Find the principal value of cos^(-1)(sqrt3/2)+cot^(-1)(1/sqrt3)+cosec^...

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  7. Find the principal value of sin^(-1)(-1/sqrt2)+tan^(-1)(-1/sqrt3)+sec^...

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  8. Find the principal value of cot^(-1)(-sqrt3)+2cosec^(-1)(-2)+cos^(-1)(...

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  9. Find the principal value of sin^(-1)(-1/sqrt2)-2tan^(-1)(-sqrt3)+cos^(...

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  10. Find tan^(-1)(3)+cot^(-1)(-1/3)+sec^(-1)2.

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  11. If tan^(-1)x+2cot^(-1)x=(5pi)/6, then find x.

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  12. Evaluate tan(cosec^(-1)(5/3)).

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  13. Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2)...

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  14. Prove that tan^(-1)(1/70)-tan^(-1)(1/99)=tan^(-1)(1/239)

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  15. Prove that cot^(-1)(13)+cot^(-1)(21)+cot^(-1)(-8)=pi.

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  16. Prove that sin^(-1)(3/5)+cos^(-1)(15/17)=cos^(-1)(36/85)

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  17. Find the value of tan { 1/2 sin^(-1) ((2x)/(1+x^(2))) + 1/2 cos^(-1...

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  18. Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if ...

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  19. Solve tan^(-1)""[(a cos x -b sinx)/(b cosx+a sinx)] , if ""(a)/(b)tan...

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  20. Evaluate 2tan^(-1)(1/2)+tan^(-1)(1/4)

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