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Show that 2 tan^-1 x = cosec^-1((1+x^2)/...

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

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Find the values of sec^-1(Sec((4pi)/3))

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

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

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  4. Solve the equation cosec^-1(x/8) + cosec ^-1 (x/15) = pi/2

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  5. Solve the equation sec^-1(x/a) - sec^-1(x/b) = sec^-1b - sec^-1 a ...

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  6. Prove that cot^-1 x = cosec^-1 sqrt(1+x^2) for x ge 0

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  7. Prove that tan(sec^-1 x) = sqrt(x^2 - 1) for x le 1

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  8. Prove that cosec^-1 x = cot^-1sqrt(x^2 -1) for x ge 1

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  9. Prove that cot(cosec^-1x) = sqrt(x^2 - 1) for x ge 1

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  10. Prove that : sec^2 (tan^(-1)2) + cosec^2 (cot^(-1) 3) = 15

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  11. Find the values of tan^2 (Sec^-1 2) + cot^2 (cosec^-1 3)

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  12. Write down the value of sin^-1{sin((7pi)/6)}

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  13. If sin^-1 x + sin^-1 y = - pi, then find the values of x and y

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  14. If sin^(-1) x + sin^(-1) y = (2pi)/3", then " cos^(-1) x + cos^(-1) y

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  15. Find the value of cos^-1(cos(-pi/4))

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  16. What ist he domain of the functio nf(x) = sin^-1 x + sec^-1 x?

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  17. What is the domain of the function f(x) = cos^-1 x + sec^-1 x?

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  18. Find the range of the function f(x) = cos^-1 x + cosec^-1 x.

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  19. Write down the domain of the function f(x) = tan^-1 x + cot^-1 x.

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  20. Find the range of the function sec^-1 x + cosec^-1 x, |x| ge 1.

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