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If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(s...

If `tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha,` then prove that `x^2=sin2alpha`

A

`(-x)/sqrt(1 - x ^(4))`

B

`(x)/sqrt(1 - x ^(4))`

C

`(-x)/sqrt(1 - x ^(2))`

D

`(x)/sqrt(1 - x ^(2))`

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A
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NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Exercies 5p
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  3. The points of discontinuity of the function f (x) = {{:(3x + 1"," ,...

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  4. If f (x) = sin (x)/(x), x ne 0 then the value of the function at x = ...

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  6. If (x) = |x| + |x - 1|, than :

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  7. Given that f(x) = {{:((sqrt(1+kx)-sqrt(1-kx))/(x),if -1 le x lt 0),(...

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  9. The function f(x)={x} , where [x] denotes the greatest integer functio...

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  10. If f(x)=(2x+3sinx)/(3x+2sinx) , x!=0 is continuous at x=0 , then find ...

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  11. If f(x)=sin^(-1) ((2x)/(1+x^2)) then f(x) is differentiable on

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  12. If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha...

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  13. d/(dx)[log{e^x((x-2)/(x+2))^(3//4)}] equals (a) (x^2-1)/(x^2-4) (b...

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  14. If x=acos^(3) theta, y=a sin^(3) theta, then ([1+((dy)/(dx))^(2)]^(3//...

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  15. If f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2)...

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  16. The derivative of the function cot^(-1){(cos2x)^(1//2)} at x=pi//6 ...

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  17. If y^(2) = ax^(2) + bx + c where a, b c are contants then y^(3)(d^(2...

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  18. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/(t^2) , then prove that (dy)/(dx)=1...

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  19. "If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...

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  20. If y = sin ^(2) alpha + cos ^(2) (alpha + beta) + 2 sin alpha sin beta...

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