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

If `tan^(-1). (sqrt((1+x^(2))) - sqrt((1-x^(2))))/(sqrt((1+x^(2)))+sqrt((1-x^(2))))=alpha" , then " x^(2) ` is

A

`cos 2 alpha`

B

`sin 2 alpha`

C

`tan 2 alpha `

D

`cot 2 alpha `

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The correct Answer is:
B
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ARIHANT MATHS-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single Option Correct Type Questions)
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  3. If tan^(-1). (sqrt((1+x^(2))) - sqrt((1-x^(2))))/(sqrt((1+x^(2)))+sqrt...

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  4. Find the number of positive integral solutions of tan^-1 x + cot^-1 y ...

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  5. If cosec^(-1) ( cosec x) " and " cosec ( cosec^(-1) x) are equal func...

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  6. The value of underset(|x| rarr oo)("lim") cos (tan^(-1) (sin (tan^(-1)...

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  7. Complete solution set of (cot^(-1)x)+2(tan^(-1)x)=0, where [] denotes ...

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  8. Prove that sin7x + sin5x + sin3x + sinx = 4cosx cos2x sin4x

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  9. If asin^(-1)x-bcos^(-1)x=c , then asin^(-1)x+bcos^(-1)x is equal to

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  10. The number of integer x satisfying sin^(-1) |x -2| + cos^(-1) (1 -|3 -...

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  11. The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),...

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  12. Prove that (cos^3x - sin^3x)/(cosx - sinx) = (2 + sin2x)/2

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  13. If alpha is the only real root of the equation x^(3) + bx^(2) + cx + 1...

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  14. Let u = cot^(-1) sqrt(cos 2 theta) - tan^(-1) sqrt( cos 2 theta) , ...

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  15. Let f(x)= cos^(-1) ((1-x^2)/(1+x^2))= 2 tan^(-1)x x ge 0 , =-2 tan^(-1...

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  16. Let f(x)= sin^(-1)((2x)/(1+x^2))AAx in R. The function f(x) is continu...

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  17. Let f: Rvec[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the s...

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  18. Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x. Then the sum of the max...

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  19. If tan^(-1) . b/(c+a) + tan^(-1) . (c)/(a + b) = pi/4where a, b, c , a...

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  20. Solutions of sin^(-1) (sinx) = sinx are if x in (0, 2pi)

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