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Solve the following equation for `x`: `tan^(-1)((2x)/(1-x^2))+cot^(-1)((1-x^2)/(2x))=(2pi)/3,x >0`

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`tan^(-1)((2x)/(1-x^2))+cot^(-1)((1-x^2)/(2x))=(2pi)/3`
`=>2tan^(-1)x+2tan^(-1)x=(2pi)/3`
`=>4tan^(-1)x=(2pi)/3`
`=>tan^(-1)x=(2pi)/6`
`=>x=tan(pi)/3`
`=>x=1/(sqrt3)`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
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  3. Solve the following equation for x: tan^(-1)((2x)/(1-x^2))+cot^(-1)...

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  4. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

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  5. Prove that: sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1

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  6. Find the principal values of (a) sin^(-1)((sqrt(3))/2) (b) sin^(-1)(...

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  7. Find the principal values of sin^(-1)(1/2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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