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Prove that: "sin"[cot^(-1){"cos"(tan^(-...

Prove that: `"sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2_1)/(x^2+2))` `"cos"[tan^(-1){"sin"(cot^(-1)x)}]=sqrt((x^2+1)/(x^2+2))`

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The value of sin [cot^(-1) {cos (tan^(-1)x)}] is :

"tan"^(-1)1/(sqrt(x^(2)-1))|x|gt1

d/dx [tan^(-1)x + sin^(-1) (x/(sqrt(1+x^(2))))] =

int_0^(1) sin (2 tan^(-1) sqrt((1+x)/(1-x))) dx =

d/(dx)[cos^(2)(cot^(-1)sqrt((2+x)/(2-x)))]

sin cot^(-1) tan cos^(-1) x is equal to :

OSWAAL PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-SHORT ANSWER TYPE QUESTIONS - II
  1. cos^(-1)((4)/(5))+cos^(-1)((12)/(13))=

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  2. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

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  3. Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^21)/(x^2+2)) ...

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  4. Prove that : 2tan^(-1)((3)/(4))-tan^(-1)((17)/(31))=(pi)/(4).

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  5. Solve for x : tan^(-1)((2x)/(1-x^2))+cot^(-1)((1-x^2)/(2x))=pi/3,-1ltx...

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  6. tan^(- 1)(1/4)+tan^(- 1)(2/9)=1/2tan^(- 1)(4/3)

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  7. solve: cos(2sin^-1x)=1/9

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  8. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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  9. (9pi)/(8)-(9)/(4)sin^(-1)""(1)/(3)=(9)/(4)sin^(-1)""(2sqrt(2))/(3) (...

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  10. Solve sin^(-1)(1-x)-2s in^(-1)x=pi/2

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  11. prove that tan^-1(1)+tan^-1(2) +tan^-1(3) = pi

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  12. Solve for x : tan^(-1)(x+2)+tan^(-1)(x-2)=tan^(-1)(8/(79)) , x >0

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  13. Solve for x:tan^(-1)((x)/(2))+tan^(-1)((x)/(3))=(pi)/(4), sqrt6gtx gt0...

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  14. prove that 2tan^-1 1/3+tan^-1 1/7=pi/4

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  15. cos^(-1)x+sin^(-1)(x/2)= pi/6

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  16. Prove the following: tan^(-1)sqrt(x)=1/2cos^(-1)((1-x)/(1+x)),\ x\ \ ...

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  17. Prove the following: tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3...

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  18. Prove the following: "cos"[tan^(-1){sin(cos t^(-1)x)}]= sqrt((1+x^2)/...

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  19. Prove that ta n^-1 1/3 + ta n ^-1 1/5 + ta n ^-1 1/7 + ta n ^-1 1/8 =...

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  20. Prove the following: tan[pi/4+1/2cos^(-1)(a/b)]+tan[pi/4-1/2cos^(-1)...

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