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Solve 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)(...

Solve `3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3`

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`2tan^(-1)x=tan^(-1)[frac{2x}{1-x^2}]=sin^(-1)[frac{2x}{1+x^2}]=cos^(-1)[frac{1-x^2}{1+x^2}]`
`3-[2tan^(-1)x]-4[2tan^(-1)x]+2[2tan^(-1)x]= (pi/3)`
`6tan^(-1)x-8tan^(-1)x+4tan^(-1)x=(pi/3)`
`tan^(-1)x=(pi/6)`
`x=frac{1}{sqrt3}`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Find the value of tan^(-1)((x-2)/(x-1))+tan^(-1)((x+2)/(x+1))=pi/4

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  2. Solve the following equation for x:tan^(-1)(1/4)+2tan^(-1)(1/5)+tan^(-...

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  3. Solve 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x...

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  4. Solve the following equation for x: tan^(-1)((2x)/(1-x^2))+cot^(-1)...

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

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  6. Solve for x : cos^(-1)((x^2-1)/(x^2+1))+1/2tan^(-1)((2x)/(1-x^2))=(2pi...

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  7. prove that 2tan^-1(sqrt((a-b)/(a+b))tan(theta/2))=cos^-1((acostheta+b)...

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  8. Show that (tan^-1)(2ab)/(a^2-b^2)+(tan^-1)(2xy)/(x^2-y^2)=(tan^-1) (2a...

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  9. For any a ,\ b ,\ x ,\ y >0 , prove that : 2/3tan^(-1)((3a b^2-a^3)/(b...

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  10. Write the value of sin^(-1)(-(sqrt(3))/2)+cos^(-1)(-1/2) .

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  11. Write the difference between maximum and minimum values of sin^(-1)...

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

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  13. If x >1 , then write the value of sin^(-1)((2x)/(1+x^2)) in terms o...

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  14. If x<0 , then write the value of cos^(-1)((1-x^2)/(1+x^2)) in terms...

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  15. Write the value of tan^(-1)x+tan^(-1)(1/x) for x >0

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  16. Write the value of tan^(-1)x+tan^(-1)(1/x) for x<0

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  17. What is the value of cos^(-1)(cos(2pi)/3)+sin^(-1)(sin(2pi)/3) ?

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  18. Write the value of sin(cot^(-1)x) .

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  19. Write the value of cos^(-1)(1/2)+2\ sin^(-1)(1/2)

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  20. The range of Tan^-1x is

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