Inverse Trigonometric Functions Questions

MathematicsInverse Trigonometric Functions30 Questions Found

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 1983Easy

View in:English Hindi

The value of $tan [cos^{- 1} (\frac{4}{5}) + tan^{- 1} (\frac{2}{3})]$ is

(A)

6/17

(B)

7/16

(C)

16/7

(D)

none

Answer:D

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 1986Easy

View in:English Hindi

The principal value of $sin^{- 1} (sin \frac{2 π}{3})$ is

(A)

2\pi/3

(B)

π /3

(C)

4\pi/3

(D)

none

Answer:B

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 1994Easy

View in:English Hindi

If we consider only the principle values of the inverse trigonometric functions then the value of $tan (cos^{- 1} \frac{1}{5 2} - sin^{- 1} \frac{4}{17})$ is

(A)

\frac{29}{3}

(B)

\frac{29}{3}

(C)

\frac{3}{29}

(D)

\frac{3}{29}

Answer:D

MathematicsSolving Inverse Trigonometric EquationsJEE Advanced 1999Moderate

View in:English Hindi

The number of real solutions of $tan^{- 1} x (x + 1) + sin^{- 1} x^{2} + x + 1 = π /2$ is

(A)

zero

(B)

one

(C)

two

(D)

infinite

Answer:C

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 2001Moderate

View in:English Hindi

If $sin^{- 1} (x - \frac{x ^{2}}{2} + \frac{x ^{3}}{4} - \dots) + cos^{- 1} (x^{2} - \frac{x ^{4}}{2} + \frac{x ^{6}}{4} - \dots) = \frac{π}{2}$ for $0 < ∣ x ∣ < 2$ , then $x$ equals

(A)

1/2

(B)

(C)

-1/2

(D)

-1

Answer:B

MathematicsDomain and Range of Inverse Trigonometric FunctionsJEE Advanced 2003Easy

View in:English Hindi

Domain of definition of the function $f (x) = sin^{- 1} (2 x) + π /6$ for real valued $x$ , is

(A)

[- 1/4, 1/2]

(B)

[- 1/2, 1/2]

(C)

[- 1/2, 1/9]

(D)

[- 1/4, 1/4]

Answer:A

MathematicsSolving Inverse Trigonometric EquationsJEE Advanced 2004Easy

View in:English Hindi

The value of $x$ for which $sin (cot^{- 1} (1 + x)) = cos (tan^{- 1} x)$ is

(A)

1/2

(B)

(C)

(D)

-1/2

Answer:D

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 2008Moderate

View in:English Hindi

$1 + x^{2} [{x cos (cot^{- 1} x) + sin (cot^{- 1} x)}^{2} - 1]^{1/2} =$

(A)

\frac{x}{1 + x ^{2}}

(B)

(C)

1 + x^{2}

(D)

1 + x^{2}

Answer:C

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 2013Moderate

View in:English Hindi

The value of $cot (\sum_{n = 1}^{23} cot^{- 1} (1 + \sum_{k = 1}^{n} 2 k))$ is

(A)

23/25

(B)

25/23

(C)

23/24

(D)

24/23

Answer:B

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 2015Moderate

View in:English Hindi

If $α = 3 sin^{- 1} (\frac{6}{11})$ and $β = 3 cos^{- 1} (\frac{4}{9})$ , where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

* Multiple Correct Options

(A)

cos β > 0

(B)

sin β < 0

(C)

cos (α + β) > 0

(D)

cos α < 0

Answer:B, C, D

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If we consider only the principle values of the inverse trigonometric functions then the value of tan(cos−152​1​−sin−117​4​) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of real solutions of tan−1x(x+1)​+sin−1x2+x+1​=π/2 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If sin−1(x−2x2​+4x3​−…)+cos−1(x2−2x4​+4x6​−…)=2π​ for 0<∣x∣<2​, then x equals

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Domain of definition of the function f(x)=sin−1(2x)+π/6​ for real valued x, is

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 1+x2​[{xcos(cot−1x)+sin(cot−1x)}2−1]1/2=

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of cot(∑n=123​cot−1(1+∑k=1n​2k)) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If α=3sin−1(116​) and β=3cos−1(94​), where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of tan[cos−1(54​)+tan−1(32​)] is

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If we consider only the principle values of the inverse trigonometric functions then the value of tan(cos−152​1​−sin−117​4​) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of real solutions of tan−1x(x+1)​+sin−1x2+x+1​=π/2 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If sin−1(x−2x2​+4x3​−…)+cos−1(x2−2x4​+4x6​−…)=2π​ for 0<∣x∣<2​, then x equals

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of x for which sin(cot−1(1+x))=cos(tan−1x) is

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If α=3sin−1(116​) and β=3cos−1(94​), where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

The value of $tan [cos^{- 1} (\frac{4}{5}) + tan^{- 1} (\frac{2}{3})]$ is

The principal value of $sin^{- 1} (sin \frac{2 π}{3})$ is

If we consider only the principle values of the inverse trigonometric functions then the value of $tan (cos^{- 1} \frac{1}{5 2} - sin^{- 1} \frac{4}{17})$ is

The number of real solutions of $tan^{- 1} x (x + 1) + sin^{- 1} x^{2} + x + 1 = π /2$ is

If $sin^{- 1} (x - \frac{x ^{2}}{2} + \frac{x ^{3}}{4} - \dots) + cos^{- 1} (x^{2} - \frac{x ^{4}}{2} + \frac{x ^{6}}{4} - \dots) = \frac{π}{2}$ for $0 < ∣ x ∣ < 2$ , then $x$ equals

Domain of definition of the function $f (x) = sin^{- 1} (2 x) + π /6$ for real valued $x$ , is

The value of $x$ for which $sin (cot^{- 1} (1 + x)) = cos (tan^{- 1} x)$ is

$1 + x^{2} [{x cos (cot^{- 1} x) + sin (cot^{- 1} x)}^{2} - 1]^{1/2} =$

The value of $cot (\sum_{n = 1}^{23} cot^{- 1} (1 + \sum_{k = 1}^{n} 2 k))$ is

If $α = 3 sin^{- 1} (\frac{6}{11})$ and $β = 3 cos^{- 1} (\frac{4}{9})$ , where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

The value of $tan [cos^{- 1} (\frac{4}{5}) + tan^{- 1} (\frac{2}{3})]$ is

The principal value of $sin^{- 1} (sin \frac{2 π}{3})$ is

If we consider only the principle values of the inverse trigonometric functions then the value of $tan (cos^{- 1} \frac{1}{5 2} - sin^{- 1} \frac{4}{17})$ is

The number of real solutions of $tan^{- 1} x (x + 1) + sin^{- 1} x^{2} + x + 1 = π /2$ is

If $sin^{- 1} (x - \frac{x ^{2}}{2} + \frac{x ^{3}}{4} - \dots) + cos^{- 1} (x^{2} - \frac{x ^{4}}{2} + \frac{x ^{6}}{4} - \dots) = \frac{π}{2}$ for $0 < ∣ x ∣ < 2$ , then $x$ equals

Domain of definition of the function $f (x) = sin^{- 1} (2 x) + π /6$ for real valued $x$ , is

The value of $x$ for which $sin (cot^{- 1} (1 + x)) = cos (tan^{- 1} x)$ is

$1 + x^{2} [{x cos (cot^{- 1} x) + sin (cot^{- 1} x)}^{2} - 1]^{1/2} =$

The value of $cot (\sum_{n = 1}^{23} cot^{- 1} (1 + \sum_{k = 1}^{n} 2 k))$ is

If $α = 3 sin^{- 1} (\frac{6}{11})$ and $β = 3 cos^{- 1} (\frac{4}{9})$ , where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)