INTRODUCTION TO TRIGONOMETRY Test

INTRODUCTION TO TRIGONOMETRY

This is INTRODUCTION TO TRIGONOMETRY Test-02 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Which of the following is true:
  • A
    \(\frac{{\cos A}}{{\sin A}} = \sec A\)
  • B
    \(\frac{{\sin A}}{{\cos ecA}} = \cot A\)
  • C
    \(\frac{{\sin A}}{{\cos A}} = \tan A\)
    Correct
  • D
    \(\frac{{\cos ecA}}{{\sin A}} = \cos A\)
2
cot A tan A =
  • A
    1
    Correct
  • B
    cot A
  • C
    sec A
  • D
    tan A
3
Given that \(\sin \theta = \frac{a}{b}\), then \(cos{\text{ }}\theta \) is equal to
  • A
    \(\frac{b}{{\sqrt {{b^2} - {a^2}} }}\)
  • B
    \(\frac{b}{a}\)
  • C
    \(\frac{{\sqrt {{b^2} - {a^2}} }}{b}\)
  • D
    \(\frac{a}{{\sqrt {{b^2} - {a^2}} }}\)
    Correct
4
The value of \(sin60^\circ cos30^\circ + sin30^\circ cos60^\circ \) is
  • A
    0
  • B
    2
  • C
    – 1
  • D
    1
    Correct
5
The value of \(2{\text{ }}ta{n^2}45^\circ + {\text{ }}co{s^2}30^\circ \;--\;si{n^2}60^\circ \) is
  • A
    1
  • B
    0
  • C
    2
    Correct
  • D
    – 2
6
If \(2sin2\theta = \sqrt 3 \) , then the value of is
  • A
    \(60^\circ \)
  • B
    \(45^\circ \)
  • C
    \(0^\circ \)
  • D
    \(30^\circ \)
    Correct
7
\(\frac{{2\tan 30^\circ }}{{1 + {{\tan }^2}30^\circ }} = \)
  • A
    \(sin60^\circ \)
    Correct
  • B
    \(\begin{array}{*{20}{l}} {cos60^\circ } \end{array}\)
  • C
    none of these
  • D
    \(tan60^\circ \)
8
\(\frac{{1 - {{\tan }^2}45^\circ }}{{1 + {{\tan }^2}45^\circ }} = \)
  • A
    0
    Correct
  • B
    \(\begin{array}{*{20}{l}} {sin45^\circ } \end{array}\)
  • C
    \(\begin{array}{*{20}{l}} {tan45^\circ } \end{array}\)
  • D
    \(cos45^\circ \)
9
sin 2A = 2 sin A is true when A =
  • A
    \(0^\circ \)
    Correct
  • B
    \(30^\circ \)
  • C
    \(\begin{array}{*{20}{l}} {45^\circ } \end{array}\)
  • D
    \(60^\circ \)
10
The value of \(\frac{{\tan 30^\circ }}{{\cot 60^\circ }}\) is
  • A
    \(\frac{1}{{\sqrt 2 }}\)
  • B
    \(\frac{1}{{\sqrt 3 }}\)
  • C
    1
    Correct
  • D
    \(\sqrt 2 \)
11
The value of \(\sin {45^ \circ } + \cos {45^ \circ }\) is
  • A
    \(\frac{1}{{\sqrt 3 }}\)
  • B
    \(\frac{1}{{\sqrt 2 }}\)
  • C
    \(\sqrt 2 \)
    Correct
  • D
    1
12
\(1 - 2{\sin ^2}30^\circ = \)
  • A
    none of these
  • B
    \(\begin{array}{*{20}{l}} {cos60^\circ } \end{array}\)
    Correct
  • C
    \(sin60^\circ \)
  • D
    \(tan60^\circ \)
13
If $~sin\text{ }\theta \text{ }=\frac{1}{2}$ and $cos\phi =\text{ }\frac{1}{2}$ , then the value of ($\theta \text{ }+\phi $ ) is
  • A
    \(\begin{array}{*{20}{l}} {90^\circ } \end{array}\)
    Correct
  • B
    \(\begin{array}{*{20}{l}} {0^\circ } \end{array}\)
  • C
    \(\begin{array}{*{20}{l}} {60^\circ } \end{array}\)
  • D
    \(\begin{array}{*{20}{l}} {30^\circ } \end{array}\)
14
Given that \(\sin \alpha = \frac{1}{{\sqrt 2 }}\) and \(\cos \beta = \frac{1}{{\sqrt 2 }}\), then the value of \((\alpha + \beta )\) is
  • A
    \(\begin{array}{*{20}{l}} {30^\circ } \end{array}\)
  • B
    \(\begin{array}{*{20}{l}} {45^\circ } \end{array}\)
  • C
    \(\begin{array}{*{20}{l}} {60^\circ } \end{array}\)
  • D
    \(\begin{array}{*{20}{l}} {90^\circ } \end{array}\)
    Correct
15
If \(\sin \alpha = \frac{1}{{\sqrt 2 }}\) and tan β = 1, then the value of \(\cos (\alpha + \beta )\) is
  • A
    0
    Correct
  • B
    3
  • C
    1
  • D
    2