Inverse Trigonometric Functions Test

Inverse Trigonometric Functions

This is Inverse Trigonometric Functions Test-02 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The value of\(\cos {15^0} - \sin {15^0}\)is
  • A
    \( - \frac{1}{{\sqrt 2 }}\)
  • B
    \(\frac{1}{{2\sqrt 2 }}\)
  • C
    \(\frac{1}{{\sqrt 2 }}\)
    Correct
  • D
    0
2
The value of \(\tan {15^0} + \cot {15^0}\)is
  • A
    Not defined.
  • B
    \(\sqrt 3 \)
  • C
    4
    Correct
  • D
    \(2\sqrt 3 \)
3
\(\sin {200^0} + \cos {200^0}\) is
  • A
    Zero
  • B
    Positive
  • C
    Negative
    Correct
  • D
    Zero or positive.
4
If\(\sin {\text{ }}A{\text{ }} + {\text{ }}\cos {\text{ }}A{\text{ }} = {\text{ }}1\), then sin 2A is equal to
  • A
    1
  • B
    2
  • C
    \(\frac{1}{2}\).
  • D
    0
    Correct
5
The value of \(\cos {105^0}\)is
  • A
    \(\frac{{1 - \sqrt 3 }}{{2\sqrt 2 }}.\)
    Correct
  • B
    \( - \frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}\)
  • C
    \(\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}\)
  • D
    \(\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}\)
6
\(\sin \left\{ {{{\sin }^{ - 1}}(\frac{{\sqrt 3 }}{5}) + {{\cos }^{ - 1}}(\frac{{\sqrt 3 }}{5})} \right\}\)is equal to
  • A
    1
    Correct
  • B
    0
  • C
    \(\frac{\pi }{2}\)
  • D
    none of these.
7
The value of the expression \(\sin \theta + \cos \theta \)lies between
  • A
    \( - \sqrt 2 \) and \(\sqrt 2 \)both inclusive
    Correct
  • B
    0 and \(\sqrt 2 \)both inclusive
  • C
    -2 and 2 both inclusive
  • D
    0 and 2 both inclusive.
8
\(\sin \left( {{{\sin }^{ - 1}}\frac{1}{2} + {{\cos }^{ - 1}}\frac{1}{2}} \right)\) equals
  • A
    0
  • B
    \(\frac{1}{2}\)
  • C
    \( - \frac{1}{4}\)
  • D
    1
    Correct
9
The range of \({\tan ^{ - 1}}\) x is
  • A
    \(\left( {\pi ,\,\,\pi } \right)\)
  • B
    R
  • C
    \(\left( {\frac{{ - \pi }}{2},\frac{\pi }{2}} \right)\)
    Correct
  • D
    \(\left( {\frac{\pi }{2}, - \frac{\pi }{2}} \right)\)
10
If \(\theta = {\tan ^{ - 1}}\)x then sin 2 θ is equal to
  • A
    \(\frac{{1 - {x^2}}}{{1 + {x^2}}}\)
  • B
    \(\frac{{2x}}{{1 - {x^2}}}\)
  • C
    None of these.
  • D
    \(\frac{{2x}}{{1 + {x^2}}}\)
    Correct
11
If \({\sin ^{ - 1}}x = \frac{\pi }{5},\) then \({\cos ^{ - 1}}x\)is equal to
  • A
    \(\frac{{3\pi }}{{10}}\)
    Correct
  • B
    \(\frac{{5\pi }}{4}\)
  • C
    \(\frac{{7\pi }}{4}.\)
  • D
    \(\frac{\pi }{{10}}\)
12
The principal value of \({\sin ^{ - 1}}(\sin \;3\pi /4) = \ldots \ldots \;\)
  • A
    \(\frac{{5\pi }}{4}\;\;\)
  • B
    \(\frac{\pi }{4}\;\;\)
    Correct
  • C
    \(\frac{{3\pi }}{4}\;\;\)
  • D
    \(\frac{{ - \pi }}{4}\;\;\)
13
\(co{t^{( - 1)}}21 + co{t^{( - 1)}}13 + co{t^{( - 1)}}( - 8)\) is equal to
  • A
    none of these
  • B
    0
    Correct
  • C
    \(\pi \)
  • D
    \({\cot ^{ - 1}}26\)
14
\(\sin ({\cot ^{ - 1}}x)\) is equal to
  • A
    \(\frac{x}{{\sqrt {1 + {x^2}} }}\)
  • B
    none of these.
  • C
    \(\sqrt {1 + {x^2}} \)
  • D
    \(\frac{1}{{\sqrt {1 + {x^2}} }}\)
    Correct
15
\({\cos ^{ - 1}}\left( {\cos \left( { - \frac{\pi }{3}} \right)} \right)\)is equal to
  • A
    \(\frac{{2\pi }}{3}\)
  • B
    \(\frac{\pi }{3}\)
    Correct
  • C
    none of these.
  • D
    \(\frac{{ - \pi }}{3}\)