INTRODUCTION TO TRIGONOMETRY Test

INTRODUCTION TO TRIGONOMETRY

This is INTRODUCTION TO TRIGONOMETRY Test-04 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The value of \(\frac{{\cos \theta \cos (90^\circ - \theta )}}{{\cot (90^\circ - \theta )}}\) is
  • A
    \({\sin ^2}\theta \)
  • B
    \({\tan ^2}\theta \)
  • C
    \(\sqrt 2 \)
    Correct
  • D
    none of these
2
If tan θ =\(\sqrt 3 \), the sec θ =
  • A
    \(\frac{1}{{\sqrt 3 }}\)
  • B
    \(\sqrt {\frac{3}{2}} \)
  • C
    2
    Correct
  • D
    \(\frac{2}{{\sqrt 3 }}\)
3
If \(\left( {\alpha {\text{ }} + {\text{ }}\beta } \right){\text{ }} = {\text{ }}90^\circ ,\) then the value of \(\sqrt {\cos \alpha \cos ec\beta - \cos \alpha \sin \beta } \) is
  • A
    \({\text{cos }}\alpha \)
  • B
    \(sin{\text{ }}\alpha \)
    Correct
  • C
    \(\cos \beta \)
  • D
    \(sin{\text{ }}\beta \)
4
\(\frac{{1 + {{\tan }^2}\theta }}{{{{\sec }^2}\theta }}\) =
  • A
    \({\sec ^2}\theta \)
  • B
    \(\frac{1}{3}\)
  • C
    1
    Correct
  • D
    \(\frac{1}{{{{\sin }^2}\theta - {{\cos }^2}\theta }}\)
5
\(\left( {{{\sec }^2}\theta - 1} \right)\left( {1 - \cos e{c^2}\theta } \right) = \)
  • A
    0
  • B
    1
  • C
    2
  • D
    – 1
    Correct
6
\({\cot ^2}\theta - \frac{1}{{{{\sin }^2}\theta }} = \)
  • A
    \({\tan ^2}\theta \)
  • B
    1
  • C
    \({\cot ^2}\theta \)
  • D
    – 1
    Correct
7
\(\sqrt {\left( {1 - {{\cos }^2}\theta } \right){{\sec }^2}\theta } \) =
  • A
    \(sin{\text{ }}\theta \)
  • B
    \(cos{\text{ }}\theta \)
  • C
    \(cot{\text{ }}\theta \)
  • D
    \(\begin{array}{*{20}{l}} {tan{\text{ }}\theta } \end{array}\)
    Correct
8
If \(\cos A + {\cos ^2}A = 1\), then the value of \({\sin ^2}A + {\sin ^4}A\) is
  • A
    2
  • B
    – 1
  • C
    0
  • D
    1
    Correct
9
\((\sec \theta + \cos \theta )(\sec \theta - \cos \theta ) = \)
  • A
    \({\tan ^2}\theta - {\sin ^2}\theta \)
  • B
    none of these
  • C
    \({\tan ^2}\theta + {\sin ^2}\theta \)
    Correct
  • D
    \({\tan ^2}\theta + {\cos ^2}\theta \)
10
The value of \(cose{c^4}A{\text{ }}--{\text{ }}2{\text{ }}cose{c^2}A{\text{ }} + {\text{ }}1\) is
  • A
    none of these
  • B
    \(co{t^4}A\)
    Correct
  • C
    \(cosee{c^4}A\)
  • D
    \(ta{n^4}A\)
11
The value of \((1 + {\tan ^2}\theta )(1 - \sin \theta )(1 + \sin \theta )\) is
  • A
    1
    Correct
  • B
    \(\sqrt 2 \)
  • C
    0
  • D
    2
12
The value of $sin^6$ A + $cos^6 $A +$ 3cos^2$ A $sin^2$ A is
  • A
    – 1
  • B
    0
  • C
    1
    Correct
  • D
    2
13
If sin A + 2 cos A = 1, then the value of 2 sin A – cos A is
  • A
    2
    Correct
  • B
    0
  • C
    – 2
  • D
    1
14
If \(\sin A + {\sin ^2}A = 1\), then the value of \({\cos ^2}A + {\cos ^4}A\) is
  • A
    0
  • B
    – 1
  • C
    1
    Correct
  • D
    2
15
\(9{\text{ }}se{c^2}A{\text{ }}--{\text{ }}9{\text{ }}ta{n^2}A{\text{ }} = \)
  • A
    1
  • B
    none of these
  • C
    9
    Correct
  • D
    0