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

Find the domain of `f(x)=sin^(-1)x+cosxdot`

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The domain of `cos` is `R` and the domain of `sin ^{-1}` is `[-1,1]`
Therefore, the domain of `cos x+sin ^{-1} x` is `R cap[-1,1]` i.e., `[-1,1]`.
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If x , y , z in [-1,1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/...

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

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  3. Find the domain of f(x)=sin^(-1)x+cosxdot

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

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

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

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

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

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  9. Prove that: 2tan^(-1)1/2+tan^(-1)1/7=tan^(-1)(31)/(17)

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  10. Solve the equation: cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/b)-cos^(-1)...

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  11. If cos^(-1)x+cos^(-1)y+cos^(-1)=pi, prove that x^2+y^2+z^2+2x y z=1.

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  12. If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(...

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  13. Solve sin^(-1)x+sin^(-1)2x=pi/3dot

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  14. Solve the following equations: sin^(-1)(3x)/5+sin^(-1)(4x)/5=sin^(-1)...

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  15. Prove that sin^(-1)(8/(17))+sin^(-1)(3/5)=cos^(-1)((36)/(85))

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  16. The value of tan^-1(1/3)+tan^-1(2/9)+tan^-1(4/33)+tan^-1(8/129)+....n ...

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  17. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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  18. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={0,ifp...

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  19. "If"sin{cot^(-1)(x+1)}=cos(tan^(-1)x), then find x.

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  20. Solve the following equation for x : "cos"(tan^(-1)x)=sin(cot^(-1)3/...

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