Inverse Trigonometric Functions Test

Inverse Trigonometric Functions

This is Inverse Trigonometric Functions Test-03 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If \(2{\tan ^{ - 1}}\left( {{\text{cos x}}} \right)\)=\({\tan ^{ - 1}}\left( {2\cos ecx} \right)\) ,then x =
  • A
    \(\frac{\pi }{3}\)
  • B
    \(\frac{\pi }{4}\)
    Correct
  • C
    none of these.
  • D
    \(\frac{\pi }{6}\)
2
\({\cos ^{ - 1}}\left( {\cos \frac{{5\pi }}{4}} \right)\)is equal to
  • A
    none of these.
  • B
    \(\frac{{3\pi }}{4}\)
    Correct
  • C
    \( - \frac{\pi }{4}\)
  • D
    \(\frac{{5\pi }}{4}\)
3
If \(co{s^{( - 1)}}x + co{s^{( - 1)}}y = 2\pi \), then the value of \(si{n^{( - 1)}}x + si{n^{( - 1)}}y\) is
  • A
    0
  • B
    \(\pi \)
  • C
    \( - \pi \)
    Correct
  • D
    none of these.
4
if \(\theta = co{s^{( - 1)}}\left( {\frac{1}{x}} \right),\) then tan θ is equal to
  • A
    \(\frac{{x\sqrt {1 - {x^2}} }}{{\left| x \right|}}\)
  • B
    none of these
  • C
    \(\sqrt {{x^2} - 1} \)
  • D
    \(\frac{{\sqrt {{x^2} - 1} }}{x}\)
    Correct
5
If \(cos(2\,si{n^{ - 1}}x) = \frac{1}{9}\)then x =
  • A
    none of these
  • B
    \( \pm \frac{2}{3}\)
    Correct
  • C
    \(\frac{2}{3}\)
  • D
    \(\frac{{ - 2}}{3}\)
6
\(2{\cos ^{ - 1}}x = {\cos ^{ - 1}}\)\(\left( {2{x^2} - 1} \right)\)holds true for all
  • A
    \(\left| x \right| \leqslant 1\)
  • B
    \(\left| x \right| \leqslant \frac{1}{2}\)
  • C
    \(0 \leqslant x \leqslant 1\)
    Correct
  • D
    none of these.
7
\({\cos ^{ - 1}}(\cos x) = x\) is satisfied by ,
  • A
    none of these.
  • B
    \(x \in [0,\pi ]\)
    Correct
  • C
    \(x \in [ - 1,1]\),
  • D
    \(x \in [0,1]\)
8
\({\tan ^{ - 1}}\frac{1}{7} + 2{\tan ^{ - 1}}\frac{1}{3}\)is equal to
  • A
    \(\frac{{3\pi }}{4}\)
  • B
    none of these.
  • C
    \(\frac{\pi }{2}\)
  • D
    \(\frac{\pi }{4}\)
    Correct
9
The value of \({\tan ^{ - 1}}\left( {\frac{a}{b}} \right) - {\tan ^{ - 1}}\left( {\frac{{a - b}}{{a + b}}} \right)\)is \(\left( {a,\,\,b > 0} \right)\)
  • A
    \( - \frac{\pi }{2}\)
  • B
    \(\frac{\pi }{2}\)
  • C
    \( - \frac{\pi }{4}\)
  • D
    \(\frac{\pi }{4}\)
    Correct
10
If \({\text{x }} > {\text{ }}0,\) then \({\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {\frac{1}{x}} \right)\)is equal to
  • A
    none of these.
  • B
    1
  • C
    tan 1
  • D
    \(\frac{\pi }{2}\)
    Correct
11
\({\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {\frac{1}{x}} \right) = \frac{\pi }{2}\) holds true for
  • A
    all \(x{\text{ }} > {\text{ 1}}\)
  • B
    all \(x \in R{\text{ }} - {\text{ }}\left\{ 0 \right\}\)
  • C
    all \(x{\text{ }} > {\text{ }}0\)
    Correct
  • D
    all \(x \in R\)
12
Which of the following is different from \(2{\tan ^{ - 1}}x\) ?
  • A
    \({\sin ^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right),\left| x \right| \leqslant 1\)
  • B
    \({\tan ^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right),\left| x \right| < 1\).
  • C
    \({\cos ^{ - 1}}\left( {\frac{{1 - {x^2}}}{{1 + {x^2}}}} \right),\left| x \right| \geqslant 0\)
  • D
    none of these
    Correct
13
\(3{\sin ^{ - 1}}x = {\sin ^{ - 1}}\)\((3x - 4{x^3})\)holds good for all
  • A
    \(\left| x \right| \leqslant \frac{1}{2}\)
    Correct
  • B
    \(\left| x \right| \leqslant 1\)
  • C
    \(0 \leqslant x \leqslant 1\)
  • D
    none of these
14
The relation \(\cos e{c^{ - 1}}\left( {\frac{{{x^2} + 1}}{{2x}}} \right) = 2{\cot ^{ - 1}}x\) is valid for
  • A
    \(x{\text{ }} \geqslant {\text{ }}0\)
  • B
    \(x{\text{ }} \geqslant {\text{ }}1\)
    Correct
  • C
    \(\left| x \right| \geqslant 1\)
  • D
    none of these.
15
If\(\left( {{{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x} \right) = \frac{\pi }{2}\), then x =
  • A
    1
  • B
    \(\frac{1}{2}\)
    Correct
  • C
    none of these.
  • D
    0