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

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

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To determine which value is greater between \( \tan(1) \) and \( \tan^{-1}(1) \), we can follow these steps: ### Step 1: Understand the values We know that \( \tan^{-1}(1) \) is the angle whose tangent is 1. The angle for which the tangent is 1 is \( \frac{\pi}{4} \) radians (or 45 degrees). Therefore, we can write: \[ \tan^{-1}(1) = \frac{\pi}{4} \] ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that: tan^(-1)1/7+tan^(-1)1/(13)=tan^(-1)2/9 tan^(-1)+tan^(-1...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. sin^(-1)(1-x)-2sin^(-1)x=pi/2 , then x is equal to (A) 0,1/2 (B) 1,1...

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  18. If y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")), prove that siny=ta...

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  19. Evaluate: tan(2tan^(-1)(1/5))

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  20. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

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