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Differentiate tan^(-1)((3a^2x-x^3)/(a^3-...

Differentiate `tan^(-1)`(`(3a^2x-x^3)/(a^3-3a x^2)`)

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Prove that:tan^(-1)sqrt(x)=1/2cos^(-1)((1-x)/(1+x)), x in [0,1]

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  2. Find the value of expression: sin(2tan^(-1)1/3)+cos(tan^(-1)2sqrt(2))

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  3. Differentiate tan^(-1)((3a^2x-x^3)/(a^3-3a x^2))

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  4. 4tan^(- 1)(1/5)=tan^(- 1)(1/70)+tan^(- 1)(1/99)+pi/4

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  5. Prove that :2tan^(-1)1/5+sec^(-1)(5sqrt(2))/7+2tan^(-1)\ 1/8=pi/4

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  6. Evaluate: tan{2t a n-1 1/5+pi/4}

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  7. Solve for x : 2tan^(-1)(cosx)=tan^(-1)(2cos e cx)

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  8. Solve sin^(-1)(1-x)-2sin ^(-1)x=pi/2

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  9. Solve: sin[2\ cos^(-1){cot(2\ tan^(-1)x)}]=0

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  10. Solve the following equation: sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

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  11. Evaluateint(2x)/(1-x^2)\dx

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  12. If cos^-1 ((x^2-1)/(x^2+1))+ tan^-1 ((2x)/(x^2-1)) = (2pi)/3, then x e...

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  13. Evaluate int(5-x).x^2\dx

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  14. Evaluateint(2-x).x^3\dx

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  15. Show taht 2tan^-1(tan(alpha/2)tan(pi/4-beta/2))=tan^-1((sinalphacosbet...

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  16. Prove that: (alpha^3)/2cos e c^2(1/2tan^(-1)(alpha/beta))+(beta^3)/2s ...

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  17. Prove that : tan^(-1){(cos2\ alphasec2\ beta+cos2betasec2alpha)/2}=tan...

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  18. Evaluate the following: (i) tan{2\ tan^(-1)(1/5)-pi/4} (ii) tan(1/2...

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  19. Evaluate the following:(i) sin(1/2\ cos^(-1)(4/5)) (ii) sin(2\ tan^...

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  20. Prove the following: 2\ sin^(-1)(3/5)=tan^(-1)(24/7)

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