Inverse Trigonometrical Functions

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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?

π/6 Signup and view all the answers

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

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

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

π + tan⁻¹ \frac{x+y}{1 - xy} Signup and view all the answers

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

tan⁻¹ \frac{x-y}{1 + xy} Signup and view all the answers

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

-π + tan⁻¹ \frac{x-y}{1 + xy} Signup and view all the answers

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

tan⁻¹ \frac{x+y+z-xyz}{1-xy-yz-zx} Signup and view all the answers

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

cot⁻¹ \frac{xy+1}{y-x} Signup and view all the answers

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

0 Signup and view all the answers

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

$\pi/6$ Signup and view all the answers

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

$\pi/4$ Signup and view all the answers

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

$\pi/6$ Signup and view all the answers

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

$\pi/3$ Signup and view all the answers

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

π/2 Signup and view all the answers

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

2π/3 Signup and view all the answers

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

π/2 Signup and view all the answers

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

π/4 Signup and view all the answers

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

π Signup and view all the answers

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

π/3 Signup and view all the answers

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

0 Signup and view all the answers

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

π/3 Signup and view all the answers

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

0 Signup and view all the answers

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

π/4 Signup and view all the answers

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

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

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

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

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

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

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

$\frac{\pi}{2}$-tan⁻¹x Signup and view all the answers

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

π/6 Signup and view all the answers

Inverse Trigonometrical Functions

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Questions and Answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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