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Find the domain of f(x)=sin^(-1)(-x^2)do...

Find the domain of `f(x)=sin^(-1)(-x^2)dot`

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Given,
`y=sin^(−1) (−x^2) implies siny= −x^2`
`therefore −1 le −x_2 le 1`
`−1 le siny le1`
`implies1ge x_2 ge −1`
`implies0 le x_2 le1`
`implies ∣x∣ le1`
`implies −1 le x le 1`

...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Find the value of sin^(-1)[cos{sin^(-1)(-(sqrt(3))/2)}] .

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  2. Find the domain of the function f(x)=sin^(-1)(2x-3) .

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  3. Find the domain of f(x)=sin^(-1)(-x^2)dot

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  4. Find the domain of f(x)=sin^(-1)x+cosx

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  5. Find the domain of the function f(x)=sin^(-1)sqrt(x-1)

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  6. If x , y , z in [-1,1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/...

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  7. Let x ,\ y ,\ z in [-1,\ 1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=(3...

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  8. Let x ,\ y ,\ z in [-1,\ 1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=(3...

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  9. Find the principal value of each of the following: (i) sin^(-1)(-(s...

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  10. Find the principal value of each of the following: (i) sin^(-1)((sq...

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  11. If tan^(-1)x = y then

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  12. Find the value of sin^(-1){cos(sin^(-1)(sqrt(3)/2))}

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  13. Find the domain of each of the following functions: (i) f(x)=sin^(-...

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  14. Find the domain of each of the following functions: (i) f(x)=sin^(-...

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  15. If sin^(-1)x+sin^(-1)y+sin^(-1)z+sin^(-1)t=2pi , then find the value ...

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  16. If (sin^(-1)x)^2+(sin^(-1)y)^2+(sin^(-1)z)^2=3/4pi^2 , find the value ...

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  17. Find the domain of cos^(-1)(2x-1)

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  18. Find the principal values of cos^(-1)((sqrt(3))/2) and cos^(-1)(-1...

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  19. Find the principal value of cos^(-1){sin"{"cos^(-1)(1/2)")"}

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  20. If x ,\ y ,\ z in [-1,1] such that cos^(-1)x+cos^(-1)y+cos^(-1)z=0 , f...

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