Inverse Trigonometric Functions Test

Inverse Trigonometric Functions

This is Inverse Trigonometric Functions Test-05 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The values of x which satisfy the trigonometric equation \({\tan ^{ - 1}}\left( {\frac{{x - 1}}{{x - 2}}} \right) + {\tan ^{ - 1}}\left( {\frac{{x + 1}}{{x + 2}}} \right) = \frac{\pi }{4}\) are :
  • A
    \( \pm \frac{1}{2}\)
  • B
    \( \pm \frac{1}{{\sqrt 2 }}\)
    Correct
  • C
    \( \pm \sqrt 2 \)
  • D
    \( \pm 2.\)
2
\({\cot ^{ - 1}}\left( {\frac{{ab + 1}}{{a - b}}} \right) + {\cot ^{ - 1}}\left( {\frac{{bc + 1}}{{b - c}}} \right) + {\cot ^{ - 1}}\left( {\frac{{ca + 1}}{{c - a}}} \right) = \)
  • A
    -1
  • B
    0
    Correct
  • C
    None of these
  • D
    1
3
The value of sin \(\left( {2{{\cos }^{ - 1}}\left( { - \frac{3}{5}} \right)} \right)\)is
  • A
    \( - \frac{{24}}{{25}}\)
    Correct
  • B
    \(\frac{{24}}{{25}}\)
  • C
    none of these.
  • D
    \(\frac{7}{{25}}\)
4
tan \(({\sin ^{ - 1}}x)\) is equal to
  • A
    none of these.
  • B
    \(\frac{x}{{\sqrt {1 - {x^2}} }}\)
    Correct
  • C
    \(\frac{{\left| x \right|}}{{\sqrt {1 - {x^2}} }}\)
  • D
    \(\frac{{ - x}}{{\sqrt {1 - {x^2}} }}\)
5
cot \(\left( {{{\cos }^{ - 1}}x} \right)\) is equal to
  • A
    \(\frac{x}{{\sqrt {1 - {x^2}} }}\)
    Correct
  • B
    none of these
  • C
    \(\frac{{ - x}}{{\sqrt {1 - {x^2}} }}\)
  • D
    \(\frac{{\left| x \right|}}{{\sqrt {1 - {x^2}} }}\)
6
cos \(({\tan ^{ - 1}}x)\)is equal to
  • A
    \(\frac{{\sqrt {1 + {x^2}} }}{x}\)
  • B
    none of these.
  • C
    \(\frac{1}{{\sqrt {1 + {x^2}} }}\)
    Correct
  • D
    \( - \frac{1}{{\sqrt {1 + {x^2}} }}\)
7
<b
Question 7 figure 1
  • A
    \(\frac{{x - y}}{{1 + xy}}\)
  • B
    \(\frac{{x + y}}{{1 - xy}}\)
    Correct
  • C
    \(\frac{1}{2}\left( {\frac{{x + y}}{{1 - xy}}} \right)\)
  • D
    \(\frac{1}{2}\left( {\frac{{x - y}}{{1 + xy}}} \right).\)
8
If \({\tan ^{ - 1}}\frac{{x - 1}}{{x + 1}} + {\tan ^{ - 1}}\frac{{2x - 1}}{{2x + 1}} = {\tan ^{ - 1}}\frac{{23}}{{36}}\) then x =
  • A
    \(\frac{4}{3}\;or\;\frac{{ - 3}}{8}\)
  • B
    \(\frac{{ - 3}}{8}\)
  • C
    \(\frac{4}{3}\)
    Correct
  • D
    none of these.
9
Question 9 figure 1
  • A
    \(\frac{\pi }{2}\)
  • B
    0
    Correct
  • C
    none of these
  • D
    \(\pi \)
10
If and \({\text{x }} + {\text{ y }} + {\text{ z }} = {\text{ xyz}},\) then a value of \({\tan ^{ - 1}}x + {\tan ^{ - 1}}y + {\tan ^{ - 1}}z\) is
  • A
    \(\pi \)
    Correct
  • B
    \(\frac{{3\pi }}{2}\)
  • C
    none of these.
  • D
    \(\frac{\pi }{2}\)
11
If and \({\text{xy }} + {\text{ yz }} + {\text{ zx }} = {\text{ }}1,\) then a value of \({\tan ^{ - 1}}x + {\tan ^{ - 1}}y + {\tan ^{ - 1}}z = \frac{\pi }{2},\) is
  • A
    \(\pi \)
  • B
    0
  • C
    \(\frac{\pi }{2}\)
    Correct
  • D
    none of these
12
If \({\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{{2\pi }}{3},then,co{s^{ - 1}}x + {\cos ^{ - 1}}y\)
  • A
    \(\frac{\pi }{3}\)
    Correct
  • B
    \(\frac{\pi }{6}\)
  • C
    \(\pi \)
  • D
    \(\frac{{2\pi }}{3}\)
13
\({\sin ^{ - 1}}\left( {\frac{3}{5}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right) = \)
  • A
    \(\pi \)
  • B
    \({\cos ^{ - 1}}\left( {\frac{4}{5}} \right)\)
  • C
    \(\frac{\pi }{2}\)
  • D
    \(\frac{\pi }{4}\)
    Correct
14
If \({\cot ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) + {\tan ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) = \mu \),then sin ยต is equal to
  • A
    1
    Correct
  • B
    \({\cot ^2}\left( {\frac{\alpha }{2}} \right).\)
  • C
    \(tan{\text{ }}2\alpha \)
  • D
    \({\tan ^2}\alpha \)
15
The value of \({\tan ^2}(se{c^{ - 1}}2) + {\cot ^2}({\operatorname{cosec} ^{ - 1}}3)\) is equal to
  • A
    5
  • B
    11
    Correct
  • C
    13
  • D
    none of these