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Prove that t a n^(-1)((cosx)/(1+sinx))=p...

Prove that `t a n^(-1)((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)`

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OSWAAL PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-SHORT ANSWER TYPE QUESTIONS - II
  1. Solve for x: tan^(-1)3x+tan^(-1)2x=pi/4

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  2. tan^(-1)((3)/(4))+tan^(-1)((3)/(5))-tan^(-1)((8)/(19))=

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  3. Prove that t a n^(-1)((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)

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  4. cos(sin^-1 (3/5)+ cot^-1(3/2)) = 6/(5sqrt13)

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  5. cos^(-1)((4)/(5))+cos^(-1)((12)/(13))=

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

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

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

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

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

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

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

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  13. (9pi)/(8)-(9)/(4)sin^(-1)""(1)/(3)=(9)/(4)sin^(-1)""(2sqrt(2))/(3) (...

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

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

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

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

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

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

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

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