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the greatest and least values of `(sin^(-1) x)^2+(cos^(-1)x)^2`

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Statement-1: sin^(-1)tan((tan^(-1))x+tan^(-1)(1-x))] =(pi)/(2) has no non zero integral solution Statement-2: The greatest and least values of (sin^(-1)x)^(3)+(cos^(-1)x)^(3) are (7pi)^(3)/(8) and (pi)^(3)/(32) respectively

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)...

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  2. Find the maximum and minimum values of (sin^(-1)x)^3+(cos^(-1)x)^3, wh...

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  3. the greatest and least values of (sin^(-1) x)^2+(cos^(-1)x)^2

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  4. Solve : 4sin^(-1)x=pi-cos^(-1)x

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  5. If (sin^(-1)x)^2+(cos^(-1)x)^2=(17pi^2)/(36) , find xdot

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. For the principal values, evaluate each of the following: "tan^(-1)sq...

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