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2 cos^-1 x = sin^-1(2xsqrt(1-x^2)) is va...

`2 cos^-1 x = sin^-1(2xsqrt(1-x^2))` is valid for all value of x satisfying:

A

`0 le x le 1/sqrt2`

B

`-1le x le 1`

C

`0 le x le 1`

D

`1/sqrt2 le x le `1

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MODERN PUBLICATION-INVERSE-TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. If tan^-1 2x + tan^-1 3x = pi/2, then the value of x is equal to

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  2. If sin^-1x + sin^-1 y + sin^-1z = (3pi)/2, then the value of x^9 + y^9...

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  3. 2 cos^-1 x = sin^-1(2xsqrt(1-x^2)) is valid for all value of x satisfy...

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  4. The number of real solutions of the equations: tan^-1 sqrt(x(x+1)) + s...

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  5. If cos^-1 x - cos^-1 y/2 = alpha, then 4x^2 - 4xy cos alpha + y^2 is e...

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  6. If sin^-1(x/5) + cosec^-1(5/4)= pi/2, then a value of x is

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  7. The value of cot(cosec^-1(5/3) + tan^-1(2/3) is

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  8. If 0 < x < 1, then : sqrt(1+x^1)[{ x cos(cot^-1x) + sin (cot^-1 x}^2 -...

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  9. If tan^(-1) y = tan^(-1) x + tan^(-1)((2x)/(1 -x^(2)))", where" |x| lt...

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  10. Find the value of sin^-1(sin(4pi)/5)

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  11. show that: 2 sin^-1(3/5) = tan^-1(24/7)

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  12. Write the value of tan^(-1)[2sin(2cos^(-1)""sqrt(3)/2)].

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  13. show that tan^-1(1/2) + tan^-1(1/5) + tan^-1(1/8) = pi/4

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  14. If tan^-1((x-2)/(x-4)) + tan^-1((x+2)/(x+4)) = pi/4 find the value of ...

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  15. Prove that : tan^-1((cosx)/(1+sinx)) = pi/4 - x/2, x in (-pi/2,pi/2)

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  16. Show that 2sin^-1(3/5)-tan^-1(17/31) = pi/4

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  17. Prove that : tan^-1 x +tan^-1 2x/(1-x^2) = tan^-1 ((3x-x^3)/(1-3x^2)),...

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  18. If tan^-1 x + tan^-1y - tan^-1z = 0, then prove that x + y + xyz = z.

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  19. Let f(x) = sin (pi/6 sin (pi/2 sinx)) for all x inR and g(x) = pi/2 si...

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  20. If alpha = 3 sin^(-1) (6/11) " and "beta = 3 cos^(-1) (4/9) , where ...

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