INTRODUCTION TO TRIGONOMETRY Test

INTRODUCTION TO TRIGONOMETRY

This is INTRODUCTION TO TRIGONOMETRY Test-01 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If \(\sin \theta = \frac{5}{{13}}\) then \(cos\theta \) =
  • A
    \(\frac{{12}}{{13}}\)
    Correct
  • B
    \(\frac{{12}}{{13}}\)
  • C
    \(\frac{{12}}{{13}}\)
  • D
    \(\frac{{\sqrt 5 }}{{13}}\)
2
If\(4{\text{ }}tan{\text{ }}\theta {\text{ }} = {\text{ }}3\) , then \(\frac{{4\sin \theta - \cos \theta }}{{4\sin \theta + \cos \theta }}\) is equal to
  • A
    \(\frac{2}{3}\)
  • B
    \(\frac{1}{2}\)
    Correct
  • C
    \(\frac{1}{3}\)
  • D
    \(\frac{3}{4}\)
3
If \(cot{\text{ }}\theta \) = \(\frac{7}{8}\), then the value of \(\frac{{(1 + \sin \theta )(1 - \sin \theta )}}{{(1 + \cos \theta )(1 - \cos \theta )}}\) is
  • A
    \(\frac{{64}}{{49}}\)
  • B
    \(\frac{{49}}{{64}}\)
    Correct
  • C
    \(\frac{7}{8}\)
  • D
    \(\frac{8}{7}\)
4
In right triangle ABC, right angled at C, if tan A = 1, then the value of 2 sin A cos A is
  • A
    2
  • B
    0
  • C
    – 1
  • D
    1
    Correct
5
In \(\Delta ABC,{\text{ }}if\;\angle B{\text{ }} = {\text{ }}90^\circ \)and cot A = 1, then the value of cos C sin A – cos A sin C is
  • A
    1
  • B
    2
  • C
    0
    Correct
  • D
    – 1
6
If \(\sin A = \frac{{12}}{{13}}\), then tan A =
  • A
    \(\frac{5}{{12}}\)
  • B
    \(\frac{{13}}{5}\)
  • C
    \(\frac{{12}}{5}\)
    Correct
  • D
    \(\frac{{13}}{{12}}\)
7
If \(tan{\text{ }}\theta \; = \) \(\frac{{20}}{{21}}\), then \(\frac{{\cos \theta - \sin \theta }}{{\cos \theta + \sin \theta }} = \)
  • A
    \(\frac{{21}}{{20}}\)
  • B
    \(\frac{1}{{21}}\)
  • C
    \(\frac{1}{{41}}\)
    Correct
  • D
    \(\frac{1}{{20}}\)
8
If 5 tan α = 4, then the value of \(\frac{{5\sin \alpha - 3\cos \alpha }}{{5\sin \alpha + 2\cos \alpha }}\) is
  • A
    \(\frac{1}{4}\)
  • B
    \(\frac{1}{5}\)
  • C
    \(\frac{1}{6}\)
    Correct
  • D
    \(\frac{4}{5}\)
9
If \(tan{\text{ }}\theta \; = \) \(\frac{a}{b}\), then \(\frac{{\cos \theta + \sin \theta }}{{\cos \theta - \sin \theta }} = \)
  • A
    \(\frac{{b + a}}{{b - a}}\)
    Correct
  • B
    none of these
  • C
    \(\frac{{b - a}}{{b + a}}\)
  • D
    \(\frac{{a - b}}{{a + b}}\)
10
If \(tan{\text{ }}\theta \; = \) \(\frac{{20}}{{21}}\), then \(\frac{{1 - \sin \theta + \cos \theta }}{{1 + \cos \theta + \sin \theta }} = \)
  • A
    \(\frac{5}{7}\)
  • B
    \(\frac{6}{7}\)
  • C
    \(\frac{4}{7}\)
  • D
    \(\frac{3}{7}\)
    Correct
11
The maximum value of \(\frac{1}{{\sec \theta }}\) is
  • A
    1
    Correct
  • B
    0
  • C
    2
  • D
    3
12
In , PR + QR = 25cm and PQ = 5cm. Then the value of sin P + tan P is
  • A
    1
  • B
    3
  • C
    4
  • D
    \(\frac{{216}}{{65}}\)
    Correct
13
If is an acute angle and\(tan{\text{ }}\theta {\text{ }} + {\text{ }}cot{\text{ }}\theta {\text{ }} = {\text{ }}2\) , then the value of \({\tan ^{25}}\theta + {\cot ^{25}}\theta \) is
  • A
    2
    Correct
  • B
    0
  • C
    1
  • D
    none of these
14
If A, B and C are interior angles of a triangle ABC, then the value of \(\tan \left( {\frac{{B + C}}{2}} \right)\) is
  • A
    none of these
  • B
    \(\tan \frac{A}{2}\)
  • C
    \(\cot \frac{A}{2}\)
    Correct
  • D
    \(\sin \frac{A}{2}\)
15
Which of the following is true:
  • A
    cos A sec A = 1
    Correct
  • B
    sin A cot A = 1
  • C
    sin A + cosec A = 1
  • D
    sin A + cos A = 1