INTRODUCTION TO TRIGONOMETRY Test

INTRODUCTION TO TRIGONOMETRY

This is INTRODUCTION TO TRIGONOMETRY Test-05 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If sec A + tan A = m and sec A – tan A = n, then the value of mn is
  • A
    0
  • B
    1
    Correct
  • C
    – 1
  • D
    2
2
5 cot2 A – 5 cosec2 A =
  • A
    1
  • B
    0
  • C
    5
  • D
    – 5
    Correct
3
\(\sqrt {\frac{{1 + \sin \theta }}{{1 - \sin \theta }}} \) =
  • A
    none of these
  • B
    \(tan{\text{ }}\theta {\text{ }}--{\text{ }}sec{\text{ }}\theta \)
  • C
    \(sec{\text{ }}\theta {\text{ }} + {\text{ }}tan{\text{ }}\theta \)
    Correct
  • D
    \(sec{\text{ }}\theta {\text{ - }}tan{\text{ }}\theta \)
4
If \(x{\text{ }} = {\text{ }}a{\text{ }}cos{\text{ }}\theta \) and\(y{\text{ }} = {\text{ }}b{\text{ }}sin{\text{ }}\theta \) , then the value of \({b^2}{x^2} + {\text{ }}{a^2}{y^2}\;\) is
  • A
    a – b
  • B
    a + b
  • C
    ab
  • D
    \(\begin{array}{*{20}{l}} {{a^2}{b^2}} \end{array}\)
    Correct
5
If \(x = a\sec \theta \cos \varphi \), \(y = b\sec \theta \sin \varphi \) and \(z = c\tan \theta \), then the value of \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}}\) is
  • A
    \(1 - \frac{{{z^2}}}{{{c^2}}}\)
  • B
    \(1 + \frac{{{z^2}}}{{{c^2}}}\)
    Correct
  • C
    none of these
  • D
    \(\frac{{{z^2}}}{{{c^2}}} - 1\)
6
If\(sec{\text{ }}\theta {\text{ }} + {\text{ }}tan{\text{ }}\theta {\text{ }} = {\text{ }}p\) , then the value of \(sin{\text{ }}\theta \) is
  • A
    \(\frac{{1 - {p^2}}}{{{p^2} + 1}}\)
  • B
    \(\frac{{{p^2} - 1}}{{{p^2} + 1}}\)
    Correct
  • C
    \(\frac{{{p^2} + 1}}{{{p^2} - 1}}\)
  • D
    none of these
7
If \(sin{\text{ }}\theta {\text{ }} + {\text{ }}cos{\text{ }}\theta {\text{ }} = {\text{ }}p\) and\(sec{\text{ }}\theta {\text{ }} + {\text{ }}cosec{\text{ }}\theta {\text{ }} = {\text{ }}q\) , then \(q\left( {{p^2}--{\text{ }}1} \right)\) =
  • A
    2p
    Correct
  • B
    none of these
  • C
    \(\frac{q}{{{p^2}}}\)
  • D
    2
8
If a \(sin{\text{ }}\theta {\text{ }} + {\text{ }}b{\text{ }}cos{\text{ }}\theta {\text{ }} = {\text{ }}c,\) then the value of a \(cos{\text{ }}\theta {\text{ }}--{\text{ }}b{\text{ }}sin{\text{ }}\theta \) is
  • A
    \(\sqrt {{a^2} + {b^2} + {c^2}} \)
  • B
    \(\sqrt {{a^2} + {b^2} - {c^2}} \)
    Correct
  • C
    \(\sqrt {{a^2} - {b^2} + {c^2}} \)
  • D
    none of these
9
If x cos A = 1 and tan A = y, then the value of \({x^2}--{\text{ }}{y^2}\) is
  • A
    2
  • B
    1
    Correct
  • C
    0
  • D
    – 1
10
If tan A = n tan B and sin A = m sin B, then cos2 A =
  • A
    \(\frac{{{m^2} - 1}}{{{n^2} - 1}}\)
    Correct
  • B
    \(\frac{{{m^2} - 1}}{{{n^2} + 1}}\)
  • C
    \(\frac{{{m^2} + 1}}{{{n^2} - 1}}\)
  • D
    \(\frac{{{m^2} + 1}}{{{n^2} + 1}}\)
11
If \(\sin \theta + \cos \theta = \sqrt 2 \cos \theta \), then the value of cos θ – sin θ is
  • A
    none of these
  • B
    \(\sqrt 2 \sin \theta \)
    Correct
  • C
    \(sin{\text{ }}\theta \)
  • D
    \(2{\text{ }}sin{\text{ }}\theta \)
12
\(1{\text{ }} + {\text{ }}\frac{{{{\cot }^2}\alpha }}{{1 + \cos ec\alpha }}{\text{ }} = \)
  • A
    \(sec{\text{ }}\alpha \)
  • B
    \(\begin{array}{*{20}{l}} {{\text{sin }}\alpha } \end{array}\)
  • C
    \(\begin{array}{*{20}{l}} {tan{\text{ }}\alpha } \end{array}\)
  • D
    \(\begin{array}{*{20}{l}} {cosec{\text{ }}\alpha } \end{array}\)
    Correct
13
\({\sin ^2}A + {\sin ^2}A{\tan ^2}A\) =
  • A
    \(co{s^2}A\)
  • B
    none of these
  • C
    \(\begin{array}{*{20}{l}} {si{n^2}A} \end{array}\)
  • D
    \(\begin{array}{*{20}{l}} {ta{n^2}A} \end{array}\)
    Correct
14
If \(\tan \theta = \frac{m}{n}\), then \(\frac{{m\sin \theta - n\cos \theta }}{{m\sin \theta + n\cos \theta }}\) =
  • A
    \(\frac{{{m^2} - {n^2}}}{{{m^2} + {n^2}}}\)
    Correct
  • B
    1
  • C
    \(\frac{{{m^2} + {n^2}}}{{{m^2} - {n^2}}}\)
  • D
    \(\frac{{{n^2} - {m^2}}}{{{n^2} + {m^2}}}\)
15
If \(\cot A + \frac{1}{{\cot A}} = 2\) then \({\cot ^2}A + \frac{1}{{{{\cot }^2}A}} = \)
  • A
    0
  • B
    – 1
  • C
    2
    Correct
  • D
    1