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Simplify cos(tan^(-1)(sin(cot^(-1)x))), ...

Simplify `cos(tan^(-1)(sin(cot^(-1)x))), x in (0,1)`.

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The correct Answer is:
`sqrt((1+x^2)/(2+x^2))`
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AAKASH INSTITUTE-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 the following (i) sin^(-1).(1)/(2) ...

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  3. Find the principal value of cot^(-1)(-sqrt3)

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  4. Find the principal value of sec^(-1)(2/sqrt3)

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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. Simplify cos(tan^(-1)(sin(cot^(-1)x))), x in (0,1).

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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. Simplity tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)(1-y^(2))/(1+y^(2)...

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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. tan^(-1)""[(a cos x -b sinx)/(b cosx+a sinx)] को सरल कीजिए, यदि ""(a)...

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

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