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Differentiate tan^(-1) sqrt((1-cos x)/(1...

Differentiate `tan^(-1) sqrt((1-cos x)/(1 + cos x)), - (pi)/(4) lt x lt (pi)/(4)`

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The correct Answer is:
`(1)/(2)`
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Short Answer Type Questions)
  1. Differentiate (x+1)^(2) (x + 2)^(3) (x + 3)^(4)

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  2. Differentiate cos^(-1) ((sin x + cos x)/(sqrt2)), - (pi)/(4) lt x lt (...

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  3. Differentiate tan^(-1) sqrt((1-cos x)/(1 + cos x)), - (pi)/(4) lt x lt...

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  4. Differentiate tan^(-1) (sec x + tan x), -(pi)/(2) lt x lt (pi)/(2)

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  5. Differentiate, tan^(-1) ((a cos x- b sin x)/(b cos x + a sin x)), (-pi...

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  6. Differentiate sec^(-1) ((1)/(4x^(3)-3x)), 0 lt x lt (1)/(sqrt2)

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  7. Write the following functions in the simplest form : tan^(-1)((3a^(2...

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  8. Prove that : tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-s...

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  9. Find (dy)/(dx): x=t + (1)/(t) and y= t - (1)/(t)

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  10. Find (dy)/(dx) of each of the functions expressed in parametric form: ...

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  11. Find (dy)/(dx) of each of the functions expressed in parametric form: ...

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  12. Find (dy)/(dx) of each of the functions expressed in parametric form: ...

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  13. Find (dy)/(dx) of each of the functions expressed in parametric form: ...

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  14. Find (dy)/(dx): x= e^(cos 2t) and y= e^(sin 2t) show that, (dy)/(dx)...

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  15. Find (dy)/(dx): x=a sin 2t (1+ cos 2t) and y= b cos 2t (1-cos 2t) ...

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  16. If x= 3 sin t- sin (3t), y= 3 cos t- cos 3t, then find ((dy)/(dx)) " ...

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  17. Differentiate (x)/(sin x) w.r.t sin x

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  18. Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t tan^(-1)x, where ...

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  19. Find (dy)/(dx) when x and y are connected by the relation given: si...

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  20. Find (dy)/(dx) when x and y are connected by the relation given: se...

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