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Prove that tan^(-1)sqrtx = 1/2cos^(-1) (...

Prove that `tan^(-1)sqrtx = 1/2cos^(-1) ((1-x)/(1+x)), x in [0,1]`

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Prove that 2 tan^-1 sqrt((1- x)/(1+x))= x, -1 le x le 1

Show that 2 tan^-1 x = cosec^-1((1+x^2)/(2x)), 0 < |x| le 1

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JMD PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXAMPLE
  1. Domain of the function f (x) = sin^-1 x is equal to :

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  2. Principal value of cos^-1 (-frac{1}{2}) is :

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  3. Find the value of tan(sin^-1 frac{3}{5} + cot^-1 frac{3}{2}).

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  4. Principal value of cos^-1 (-frac{1}{2}) is :

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  5. Find dy/dx when: y= tan^-1((2x)/(1-x^2))

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

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  7. Prove that sqrt((1+sinA)/(1-sinA))=(1+sinA)/cosA .

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  8. Show that : tan^-1 frac{1}{3} + tan^-1 frac{1}{5}=frac{1}{2} cos^-1 fr...

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  9. Prove that : tan^(-1) (1) + tan ^-1 (2) + tan^(-1) (3) = pi1

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

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  11. Show that: tan^-1 (frac {1-x}{1+x})= frac {1}{2} tan^-1(frac{1-x^2}{2x...

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  12. Prove that : 2 tan^-1 frac{1}{5} + tan^-1 frac{1}{8}= tan^-1 frac{4}{7...

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  13. Prove that : tan^-1[(sqrt(1+x) - sqrt(1-x))/(sqrt1+x + sqrt1-x)] = pi/...

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  14. Find the value 2 tan^(-1)(1/5) + sec^(-1) ((5sqrt2)/7)+ 2tan^(-1)(1/8)

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  15. Prove that : sin^-1 (frac{3}{5}) + cos^-1 (frac{5}{sqrt26}) = tan^-1 (...

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  16. Solve for x: tan^-1 (x+1) + tan^-1(x-1) = tan^-1 frac{8}{31}, x > 0

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  17. Prove that : cos^-1 frac{12}{13} + sin^-1 frac{4}{5}= tan^-1 frac{63}{...

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

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  19. tan^-1 frac{63}{16}= sin^-1 frac{5}{13}+cos^-1 frac{3}{5}

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

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