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For any a ,\ b ,\ x ,\ y >0 , prove that...

For any `a ,\ b ,\ x ,\ y >0` , prove that : `2/3tan^(-1)((3a b^2-a^3)/(b^3-3a^2b))+2/3tan^(-1)((3x y^2-x^3)/(y^3-3x^2y))=tan^(-1)(2alphabeta)/(alpha^2-beta^2)` , where `alpha=-a x+b y` `beta=b x+a ydot`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
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  3. For any a ,\ b ,\ x ,\ y >0 , prove that : 2/3tan^(-1)((3a b^2-a^3)/(b...

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

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

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

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

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

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

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

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

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  12. write the value of sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) .

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

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

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  15. The range of Tan^-1x is

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  18. Write the value of cos(2\ sin^(-1)1/3) .

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  19. Write the value of sin^-1(sin1550^@)

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  20. Evaluate sin(1/2cos^(-1)(4/5))

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