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Prove that: sin^(-1)(12)/(13)+cos^(-1)4/...

Prove that: `sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi`

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To prove that \[ \sin^{-1}\left(\frac{12}{13}\right) + \cos^{-1}\left(\frac{4}{5}\right) + \tan^{-1}\left(\frac{63}{16}\right) = \pi, \] we will denote: ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

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  2. Prove that : tan^(-1)(2/11)+tan^(-1)(7/24)=tan^(-1)(1/2)

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  3. Prove that: sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi

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  4. Prove that: tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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  5. Prove that: tan^(-1)1/7+tan^(-1)1/(13)=tan^(-1)2/9 tan^(-1)+tan^(-1...

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  6. If tan^(-1)2+tan^(-1)3+theta=pi, find the value of thetadot

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  7. What is greater, tan1 or tan^(-1)1?

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  8. Find the minimum value of n for which tan^(-1)(n/pi)>pi/4,n in Ndo...

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  9. Find the principal values of sec^(-1)2/(sqrt(3)) and sec^(-1)(-2)

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  10. Find the domain of sec^(-1)(2x+1)

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  11. Find the principal value of cos^(-1){sin"{"cos^(-1)1/2")"}

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  12. If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then...

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  13. Evaluate tan ^ (-1) {sin (-pi/2)}

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  14. For the principal values, evaluate each of the following: tan^(-1){2co...

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  15. For the principal values, evaluate each of the following: tan^(-1)sqr...

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  16. Find the domain of sec^(-1)(3x-1) + sec^(-1)x-tan^(-1)x

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  17. Show that cos^(-1) ((cos alpha+cos beta)/(1+cosalpha cosbeta))=2 tan^(...

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

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  19. Prove the following: 4tan^(-1)1/5-tan^(-1)1/(70)+tan^(-1)1/(99)=pi/4 ...

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  20. Evaluate: tan{1/2cos^(-1)(sqrt5/3)}

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