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Prove the following : tan^(-1)sqrtx=1/2 ...

Prove the following :
`tan^(-1)sqrtx=1/2 cos^(-1)((1-x)/(1+x)),x in[0,1]`

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BODY BOOKS PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Find the principal value of sec^-1(-frac(2)(sqrt3))

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  2. Prove : tan^-1x=sec^-1sqrt(1+x^2).

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  3. Prove the following : tan^(-1)sqrtx=1/2 cos^(-1)((1-x)/(1+x)),x in[0,1...

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  4. Show that tan^-1(x/(sqrt(a^2-x^2)))=sin^-1(x/a)

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  5. Find the principal value of cos^-1(frac(sqrt3)(2))

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  6. In proving the result 3sin^-1x=sin^-1(3x-4x^3) Substitute x=

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  7. Prove that 3 sin ^(-1) x = sin^(-1) (3x - 4x^3), x in [-1/2,1/2]

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  8. Within the domain of definitions prove that sin^-1(-x)=-sin^-1x

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  9. tan^-1(tantheta)=

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  10. Show that tan^-1(costheta/(1+sintheta)) is independent of trigonometri...

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  11. Prove that 2tan^-1(1/3)+tan^-1(1/7)=pi/4.

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  12. If xy<1,tan^-1x+tan^-1y=........ a)tan^-1(frac(x-y)(1+xy)) b)tan^-1(f...

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  13. Solve tan^-1 2x+tan^-1 3x=pi/4

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  14. If A=sin^-1frac(2x)(1+x^2) , B=cos^-1frac(1-x^2)(1+x^2) , C=tan^-1frac...

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  15. Prove that tan^-1 (1/2)+tan^-1(2/11)=tan^-1(3/4)

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  16. Principal value of cot^-1(-1/(sqrt3)) is a)pi/3 b)-pi/3 c)pi/6 d)2pi/3

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  17. If tan^(-1) ((x-1)/(x-2)) + tan^(-1) ((x+1)/(x+2)) = pi/4. then find t...

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  18. If xy<1,tan^-1x+tan^-1y=........ a)tan^-1(frac(x-y)(1+xy)) b)tan^-1(f...

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  19. Prove that 2 tan^(-1)(1/2) + tan^(-1)(1/7) = tan^(-1)(31/17)

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  20. What is the value of sin^-1(sin160^@)?

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