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Solve the following equations. cos^-1(...

Solve the following equations.
`cos^-1((1-x^2)/(1+x^2)) + tan^-1 ((2x)/(1-x^2)) = (2pi)/3, 0 le x < 1`

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Solve the following equations: tan^-1((1-x)/(1+x)) = 1/2 tan^-1 x, x...

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

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  3. Solve the following equations. cos^-1((1-x^2)/(1+x^2)) + tan^-1 ((2x...

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  4. Solve : 3 tan^-1(1/(2+sqrt3)) - tan^-1(1/x) = tan^-1(1/3)

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  5. Solve the following equations. tan^-1 (x-1) + tan^-1 x + tan^-1 (x+1...

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  6. Solve the following equations. tan^-1 (sqrt(x^2 + x) + sin^-1 sqrt(x...

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  7. Solve the following equations. tan^-1 (x-1)/(x-2) + tan6-1 (x+1)/(x+...

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  8. Solve : ((tan^-1 ((2x-3)/(2x-5)) + tan^-1((2x+3)/(2x+5)))=pi/4) .

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  9. Solve the following equations. cos(tan^-1x) = sin (cot^-1 (3//4)

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  10. Solve the following equations: tan^-1(x+1) + tan^-1 (x-1) = tan^-1 (...

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  11. Prove that for 0 < a < b < c cot^-1 (1+ab)/(a-b) + cot^-1 (1+bc)/(b-...

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  12. If tan^-1x + tan^-1y + tan^-1z = pi, then prove that: x + y + z = xyz.

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  13. Find the value of the following: tan1/2[sin^-1(2x/(1+x^2)) + cos^-1(1-...

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  14. Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^...

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

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  16. If x in R, find the maximum and minimum values of 2 tan^-1 x + sin^-1 ...

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  17. Find the values of sec^-1( 2/sqrt3)

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  18. Find the values of sec^-1(Sec((4pi)/3))

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  19. Find the values of cot (cosec^-1 (-1))

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  20. Show that 2 tan^-1 x = cosec^-1((1+x^2)/(2x)), 0 < |x| le 1

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