Inverse Trigonometrical Functions
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Questions and Answers

What is the domain of sin^(-1) x?

  • (-1, 1) (correct)
  • (-∞, ∞)
  • (-π, π)
  • [0, 1]

What is the range of tan^(-1) x?

  • (0, π)
  • (-π/2, π/2) (correct)
  • (-π, π)
  • (-∞, ∞)

What is the value of cosec^(-1) (1/x) in terms of x?

  • cot^(-1) x (correct)
  • sec^(-1) x
  • sin^(-1) x
  • tan^(-1) x

What is the value of sin^(-1) (1/2) in terms of π?

<p>π/6 (A)</p> Signup and view all the answers

What is the value of cot^(-1) (x) in terms of tan^(-1) x?

<p>π/2 - tan^(-1) x (C)</p> Signup and view all the answers

If x > 0, y > 0 and xy > 1, what is the value of tan⁻¹x + tan⁻¹y?

<p>π + tan⁻¹ \frac{x+y}{1 - xy} (D)</p> Signup and view all the answers

If x < 0, y < 0 and xy > 1, what is the value of tan⁻¹x - tan⁻¹y?

<p>tan⁻¹ \frac{x-y}{1 + xy} (B)</p> Signup and view all the answers

If x > 0, y < 0 and xy < -1, what is the value of tan⁻¹x - tan⁻¹y?

<p>-π + tan⁻¹ \frac{x-y}{1 + xy} (C)</p> Signup and view all the answers

If x, y, z are positive, what is the value of tan⁻¹x + tan⁻¹y + tan⁻¹z?

<p>tan⁻¹ \frac{x+y+z-xyz}{1-xy-yz-zx} (D)</p> Signup and view all the answers

If x, y are positive, what is the value of cot⁻¹x + cot⁻¹y?

<p>cot⁻¹ \frac{xy+1}{y-x} (C)</p> Signup and view all the answers

What is the value of $tan^{-1} (tan(\pi/4) - tan(\pi/4))$?

<p>0 (B)</p> Signup and view all the answers

If $tan^{-1} x = \pi/3$, what is the value of $tan^{-1} (1/x)$?

<p>$\pi/6$ (B)</p> Signup and view all the answers

What is the value of $cos^{-1} (1/\sqrt{2})$?

<p>$\pi/4$ (C)</p> Signup and view all the answers

If $sin^{-1} x = \pi/6$, what is the value of $sin^{-1} (\sqrt{1 - x^2})$?

<p>$\pi/6$ (A)</p> Signup and view all the answers

What is the value of $cot^{-1} (\sqrt{3})$?

<p>$\pi/3$ (A)</p> Signup and view all the answers

What is the value of tan⁻¹(x) + tan⁻¹(1/x)?

<p>π/2 (B)</p> Signup and view all the answers

If cot⁻¹(x) = π/3, what is the value of cot⁻¹(1/x)?

<p>2π/3 (A)</p> Signup and view all the answers

What is the value of sin⁻¹(x) + sin⁻¹(1/x)?

<p>π/2 (C)</p> Signup and view all the answers

If tan⁻¹(x) = π/4, what is the value of tan⁻¹(√(1-x²))?

<p>π/4 (A)</p> Signup and view all the answers

What is the value of cos⁻¹(x) + cos⁻¹(1/x)?

<p>π (C)</p> Signup and view all the answers

If cot⁻¹(x) = π/6, what is the value of cot⁻¹(√(1+x²))?

<p>π/3 (A)</p> Signup and view all the answers

What is the value of sin⁻¹(x) - sin⁻¹(1/x)?

<p>0 (C)</p> Signup and view all the answers

If tan⁻¹(x) = π/3, what is the value of tan⁻¹(1/√(1+x²))?

<p>π/3 (A)</p> Signup and view all the answers

What is the value of cos⁻¹(x) - cos⁻¹(1/x)?

<p>0 (C)</p> Signup and view all the answers

If cot⁻¹(x) = π/4, what is the value of cot⁻¹(1/√(1-x²))?

<p>π/4 (A)</p> Signup and view all the answers

If x, y are positive and xy < 1, what is the value of tan⁻¹x + tan⁻¹y?

<p>tan⁻¹((x+y)/(1-xy)) (B)</p> Signup and view all the answers

If x, y, z are positive, what is the value of tan⁻¹x + tan⁻¹y + tan⁻¹z?

<p>tan⁻¹((x+y+z-xyz)/(1-xy-yz-zx)) (D)</p> Signup and view all the answers

If x, y are positive, what is the value of cot⁻¹x + cot⁻¹y?

<p>cot⁻¹((xy+1)/(y-x)) (C)</p> Signup and view all the answers

What is the value of cot⁻¹x in terms of tan⁻¹x?

<p>$\frac{\pi}{2}$-tan⁻¹x (A)</p> Signup and view all the answers

If cot⁻¹x = π/3, what is the value of cot⁻¹(1/√(1-x²))?

<p>π/6 (D)</p> Signup and view all the answers

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