Inverse Trigonometric Functions Questions

MathematicsInverse Trigonometric Functions30 Questions Found

MathematicsSolving Inverse Trigonometric EquationsJEE Advanced 2007Moderate

Let $(x, y)$ be such that $sin^{- 1} (a x) + cos^{- 1} (y) + cos^{- 1} (b x y) = \frac{π}{2}$ . Match the statements in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the ORS.

List-I

(P)

a = 1

and

b = 0

, then

(x, y)

(Q)

a = 1

and

b = 1

, then

(x, y)

(R)

a = 1

and

b = 2

, then

(x, y)

(S)

a = 2

and

b = 2

, then

(x, y)

List-II

(1)

lies on the circle

x^{2} + y^{2} = 1

(2)

lies on

(x^{2} - 1) (y^{2} - 1) = 0

(3)

lies on

y = x

(4)

lies on

(4 x^{2} - 1) (y^{2} - 1) = 0

Answer:P → 1, Q → 2, R → 1, S → 4

MathematicsSolving Inverse Trigonometric EquationsJEE Advanced 2013Moderate

View in:English Hindi

Match List I with List II:

List-I

(P)

[\frac{1}{y ^{2}} (\frac{c o s ( t a n ^{- 1} y ) + y s i n ( t a n ^{- 1} y )}{c o t ( s i n ^{- 1} y ) + t a n ( s i n ^{- 1} y )})^{2} + y^{4}]^{1/2}

takes value

(Q)

cos x + cos y + cos z = 0 = sin x + sin y + sin z

then possible value of

cos \frac{x - y}{2}

(R)

cos (\frac{π}{4} - x) cos 2 x + sin x sin 2 x sec x = cos x sin 2 x sec x + cos (\frac{π}{4} + x) cos 2 x

then possible value of

sec x

(S)

cot (sin^{- 1} 1 - x^{2}) = sin (tan^{- 1} (x 6))

x \neq = 0

, then possible value of

x

List-II

(1)

\frac{1}{2} \frac{5}{3}

(2)

2

(3)

\frac{1}{2}

(4)

Answer:P → 4, Q → 3, R → 2, S → 1

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 1993Moderate

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Using mathematical induction, prove that $tan^{- 1} (1/3) + tan^{- 1} (1/7) + .... tan^{- 1} {1/ (n^{2} + n + 1)} = tan^{- 1} {n / (n + 2)}$

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 2002Easy

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Prove that $cos tan^{- 1} sin cot^{- 1} x = \frac{x ^{2} + 1}{x ^{2} + 2}$ .

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 1981Easy

View in:English Hindi

Find the value of : $cos (2 cos^{- 1} x + sin^{- 1} x)$ at $x = \frac{1}{5}$ , where $0 \leq cos^{- 1} x \leq π$ and $- π /2 \leq sin^{- 1} x \leq π /2$ .

Answer:

- \frac{2 6}{5}

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 1984Easy

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The numerical value of $tan {2 tan^{- 1} (\frac{1}{5}) - \frac{π}{4}}$ is equal to .........

Answer:

- \frac{7}{17}

MathematicsDomain and Range of Inverse Trigonometric FunctionsJEE Advanced 1984Moderate

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The domain of the function $f (x) = sin^{- 1} (lo g_{2} \frac{x ^{2}}{2})$ is given by .........

Answer:

[- 2, - 1] \cup [1, 2]

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 1989Moderate

View in:English Hindi

The greater of the two angles $A = 2 tan^{- 1} (22 - 1)$ and $B = 3 sin^{- 1} (1/3) + sin^{- 1} (3/5)$ is .........

Answer:A

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 1981Moderate

View in:English Hindi

Let $a, b, c$ be positive real numbers. Let $θ = tan^{- 1} \frac{a ( a + b + c )}{b c} + tan^{- 1} \frac{b ( a + b + c )}{c a} + tan^{- 1} \frac{c ( a + b + c )}{ab}$ . Then $tan θ =$ .........

Answer:0

MathematicsProperties of Inverse Trigonometric FunctionsJEE Advanced 2014Moderate

View in:English Hindi

Let $f : [0, 4 π] \to [0, π]$ be defined by $f (x) = cos^{- 1} (cos x)$ . The number of points $x \in [0, 4 π]$ satisfying the equation $f (x) = \frac{10 - x}{10}$ is

Answer:3

List-I

List-II

Match List I with List II:

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Using mathematical induction, prove that tan−1(1/3)+tan−1(1/7)+....tan−1{1/(n2+n+1)}=tan−1{n/(n+2)}

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Prove that costan−1sincot−1x=x2+2x2+1​​.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the value of : cos(2cos−1x+sin−1x) at x=51​, where 0≤cos−1x≤π and −π/2≤sin−1x≤π/2.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The numerical value of tan{2tan−1(51​)−4π​} is equal to .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The domain of the function f(x)=sin−1(log2​2x2​) is given by .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The greater of the two angles A=2tan−1(22​−1) and B=3sin−1(1/3)+sin−1(3/5) is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let a,b,c be positive real numbers. Let θ=tan−1bca(a+b+c)​​+tan−1cab(a+b+c)​​+tan−1abc(a+b+c)​​. Then tanθ= .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let f:[0,4π]→[0,π] be defined by f(x)=cos−1(cosx). The number of points x∈[0,4π] satisfying the equation f(x)=1010−x​ is

List-I

List-II

Match List I with List II:

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Using mathematical induction, prove that tan−1(1/3)+tan−1(1/7)+....tan−1{1/(n2+n+1)}=tan−1{n/(n+2)}

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Prove that costan−1sincot−1x=x2+2x2+1​​.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the value of : cos(2cos−1x+sin−1x) at x=51​, where 0≤cos−1x≤π and −π/2≤sin−1x≤π/2.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The numerical value of tan{2tan−1(51​)−4π​} is equal to .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The domain of the function f(x)=sin−1(log2​2x2​) is given by .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The greater of the two angles A=2tan−1(22​−1) and B=3sin−1(1/3)+sin−1(3/5) is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let a,b,c be positive real numbers. Let θ=tan−1bca(a+b+c)​​+tan−1cab(a+b+c)​​+tan−1abc(a+b+c)​​. Then tanθ= .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let f:[0,4π]→[0,π] be defined by f(x)=cos−1(cosx). The number of points x∈[0,4π] satisfying the equation f(x)=1010−x​ is

Using mathematical induction, prove that $tan^{- 1} (1/3) + tan^{- 1} (1/7) + .... tan^{- 1} {1/ (n^{2} + n + 1)} = tan^{- 1} {n / (n + 2)}$

Prove that $cos tan^{- 1} sin cot^{- 1} x = \frac{x ^{2} + 1}{x ^{2} + 2}$ .

Find the value of : $cos (2 cos^{- 1} x + sin^{- 1} x)$ at $x = \frac{1}{5}$ , where $0 \leq cos^{- 1} x \leq π$ and $- π /2 \leq sin^{- 1} x \leq π /2$ .

The numerical value of $tan {2 tan^{- 1} (\frac{1}{5}) - \frac{π}{4}}$ is equal to .........

The domain of the function $f (x) = sin^{- 1} (lo g_{2} \frac{x ^{2}}{2})$ is given by .........

The greater of the two angles $A = 2 tan^{- 1} (22 - 1)$ and $B = 3 sin^{- 1} (1/3) + sin^{- 1} (3/5)$ is .........

Let $a, b, c$ be positive real numbers. Let $θ = tan^{- 1} \frac{a ( a + b + c )}{b c} + tan^{- 1} \frac{b ( a + b + c )}{c a} + tan^{- 1} \frac{c ( a + b + c )}{ab}$ . Then $tan θ =$ .........

Let $f : [0, 4 π] \to [0, π]$ be defined by $f (x) = cos^{- 1} (cos x)$ . The number of points $x \in [0, 4 π]$ satisfying the equation $f (x) = \frac{10 - x}{10}$ is

Using mathematical induction, prove that $tan^{- 1} (1/3) + tan^{- 1} (1/7) + .... tan^{- 1} {1/ (n^{2} + n + 1)} = tan^{- 1} {n / (n + 2)}$

Prove that $cos tan^{- 1} sin cot^{- 1} x = \frac{x ^{2} + 1}{x ^{2} + 2}$ .

Find the value of : $cos (2 cos^{- 1} x + sin^{- 1} x)$ at $x = \frac{1}{5}$ , where $0 \leq cos^{- 1} x \leq π$ and $- π /2 \leq sin^{- 1} x \leq π /2$ .

The numerical value of $tan {2 tan^{- 1} (\frac{1}{5}) - \frac{π}{4}}$ is equal to .........

The domain of the function $f (x) = sin^{- 1} (lo g_{2} \frac{x ^{2}}{2})$ is given by .........

The greater of the two angles $A = 2 tan^{- 1} (22 - 1)$ and $B = 3 sin^{- 1} (1/3) + sin^{- 1} (3/5)$ is .........

Let $a, b, c$ be positive real numbers. Let $θ = tan^{- 1} \frac{a ( a + b + c )}{b c} + tan^{- 1} \frac{b ( a + b + c )}{c a} + tan^{- 1} \frac{c ( a + b + c )}{ab}$ . Then $tan θ =$ .........

Let $f : [0, 4 π] \to [0, π]$ be defined by $f (x) = cos^{- 1} (cos x)$ . The number of points $x \in [0, 4 π]$ satisfying the equation $f (x) = \frac{10 - x}{10}$ is