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Prove that tan^-1((sqrt(1+x)- (sqrt(1-...

Prove that
`tan^-1((sqrt(1+x)- (sqrt(1-x)))/(sqrt(1+x) + (sqrt(1-x)))) = pi/4 - 1/2 cos^-1 x`

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Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^2))] = pi/4 - 1/2cos^-1x^2

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Show that: tan^(-1)[(sqrt(1+x^(2)) + sqrt(1-x^(2)))/(sqrt(1 +x^(2))- sqrt(1-x^(2)))]=pi/4 +1/2 cos^(-1) x^(2), -1 lt x lt 1

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Prove that tan^(-1)sqrtx = 1/2cos^(-1) ((1-x)/(1+x)), x in [0,1]

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  2. Prove that : cot^-1[(sqrt(1+sin x) + sqrt(1-sin x))/(sqrt1+sin x + sqr...

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  3. Prove that tan^-1((sqrt(1+x)- (sqrt(1-x)))/(sqrt(1+x) + (sqrt(1-x)))...

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  4. Prove that (9pi)/8 - 9/4 sin^-1 (1/3) = 9/4 si^-1 ((2sqrt2)/3)

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  5. Solve the 2 tan^-1 (cos x) = tan^-1 (2 cosec x).

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  6. Solve the following equations: tan^-1((1-x)/(1+x)) = 1/2 tan^-1 x, x...

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  7. sin(tan^-1x), |x|<1 is equal to :

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  8. If sin^-1(1-x) - 2sin^-1x = pi/2, then x is equal to :

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  9. tan^-1(x/y)-tan^-1((x-y)/(x+y)) is equal to :

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  10. Fill in the blanks: Domain of the function sin^-1 x is ……..

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  11. Range of function cos^-1 x is :

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  12. The principal value of tan^(-1)sqrt(3) is ............... .

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  13. Find the value of sin^-1(sin (3pi/5))

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  14. Fill in the blanks: Principal value of the function tan^-1 x lie in ...

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  15. Fill in the blanks: tan^-1 1 + sin^-1 (-sqrt3/2) + cos^-1 (-sqrt3/2)...

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  16. Principal value of cos^-1 (-1/2) is :

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  17. Fill in the blanks: The value of cos^-1 (cos 14pi/3) is …………

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  18. Fill in the blanks: The set of values of sec^-1 (1/2) is ……………

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  19. Fill in the blanks: For x in R, tan^-1 (x^2 +1) + cot^-1 (x^2 +1) is...

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  20. Fill in the blanks: If cos^-1 (-x) = alpha - cos^-1 x, then the valu...

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