Chapter 8: Fundamentals of Trigonometry – MCQs Test | National Book Foundation

Chapter 8: Fundamentals of Trigonometry – MCQs Preparation Test | National Book Foundation

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Chapter 8: Fundamentals of Trigonometry, designed for 1st-year students.

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Chapter 8: Fundamentals of Trigonometry | National Book Foundation

July 2, 2026

Name

Class

$2\sin {\frac{P+Q}{2}\cos {\frac{P-Q}{2}}}$

$\sin P - \sin Q$

$\cos P - \cos Q$

$\cos P + \cos Q$

$\sin P + \sin Q$

None

$\tan (\frac{3\pi}{2}+\theta)=$______

$-\tan {\theta}$

$\tan {\theta}$

$\cot {\theta}$

$-\cot {\theta}$

None

$\sin (\theta - 270^\circ)$

$\sin {\theta}$

$-\sin {\theta}$

$\cos {\theta}$

$-\cos {\theta}$

None

If $r \cos {\theta} =3$, $r \sin {\theta} =4$, then $r=$________

$25$

$5$

$-25$

$-5$

None

Distance between $A(3,8) , B(5,6)$ is ______

$2$

$\frac{1}{2}$

$\sqrt{2}$

$2\sqrt{2}$

None

$\sin (-\alpha)=?$

$\csc (\alpha)$

$-\sin (\alpha)$

$\cos (\alpha)$

$\sin (\alpha)$

None

The angle associated with basic angles of the measure $\theta$ a right angle or its multiple are called _________

supplementary

Complementary

Quadrantal

Obtuse

None

$2\sin {\alpha} \cos {\alpha}$

$\sin 2(\pi-\alpha)$

$\sin (\pi+2\alpha)$

$\sin (\pi-2\alpha)$

$\sin (-2\alpha)$

None

$\frac{2 \tan{\theta}}{1-\tan^2 {\theta}}$ is equal to:

$\cot {2\theta}$

$\cos {2\theta}$

$\tan {2\theta}$

$\sin {2\theta}$

None

10.

$\sin {3\alpha}$ equal to:

$4 \sin^3 {\alpha}+3\sin {\alpha}$

$4 \sin^3 {\alpha}-3\sin {\alpha}$

$3 \sin {\alpha}-4\sin^3 {\alpha}$

$3 \sin {\alpha}+4\sin^3 {\alpha}$

None

11.

$\cos (\pi -\theta)=?$

$\pm \cos {\theta}$

$\sec {\theta}$

$\cos {\theta}$

$-\cos {\theta}$

None

12.

$\cos {319^\circ}$ is equal to

$\sin {41^\circ}$

$\cos {41^\circ}$

$\cos {49^\circ}$

zero

None

13.

$\sin {\theta}=$

$2\cos^2 {\frac{\theta}{2}}$

$2\sin {\frac{\theta}{2}}\cos {\frac{\theta}{2}}$

$2\tan {\frac{\theta}{2}}$

$2\sin^2 {\frac{\theta}{2}}$

None

14.

The angle $90^{\circ} \pm \theta$ , $180^{\circ} \pm \theta$, $270^{\circ} \pm \theta$, $360^{\circ} \pm \theta$, are the ____ angles,

quadrantal

composite

half

allied

None

15.

If $\cos {\theta}=-\frac{\sqrt{3}}{2}$ and the terminal arm of angles in III quadrant. Then $\sin {\theta}=$_____.

$\frac{-2}{\sqrt{3}}$

$\sqrt{3}$

$\frac{1}{2}$

$-\frac{1}{2}$

None

16.

$\sin {2\alpha}$ is equal to ____

$1-2\sin^2{\alpha}$

$2\sin^2{\alpha}-1$

$\sin {\alpha}$

$2\sin {\alpha} \cos{\alpha}$

None

17.

$\frac{\cos{11^\circ}+\sin11^{\circ}}{\cos{11^\circ}-\sin11^{\circ}}$

$\tan {11^\circ}$

$\cot {56^\circ}$

$\tan {56^\circ}$

$\cot {11^\circ}$

None

18.

$\cos (60^{\circ}-30^{\circ}) \neq ?$

$\cos 330^{\circ}$

$\sqrt {1-\sin^2 30^{\circ}}$

$\cos 30^{\circ}$

$\sin 30^{\circ}$

None

19.

$\cos (\alpha +\beta)-\cos(\alpha -\beta)=$_________

$2\cos {\alpha} \sin {\beta}$

$-2\sin {\alpha} \sin {\beta}$

$2\cos {\alpha} \cos {\beta}$

$2\sin {\alpha} \cos {\beta}$

None

20.

$\frac{3\pi}{2}+10^{\circ}$ lies in:

$4^{\text{th}}$

$3^{\text{rd}}$

$1^{\text{st}}$

$2^{\text{nd}}$

None

21.

The trigonometric identity $\frac{\sin{\alpha}+\sin{2\alpha}}{1+\cos{\alpha}+\cos{2\alpha}}=$_______.

$\cos{\alpha}$

$\cot{\alpha}$

$\sin{\alpha}$

$\tan{\alpha}$

None

22.

$\sin {3\theta} -\sin {5\theta}$ equals ____.

$2 \sin {4\theta} \cos {\theta}$

$2 \sin {\theta} \cos {4\theta}$

$-2 \sin {\theta} \cos {4\theta}$

$2 \sin {4\theta} \cos {2\theta}$

None

23.

If $ 2\sin {\theta} + \frac{1}{2} \csc{\theta}$ and $\theta=45^{\circ}$, then the value of the given trigonometric identity is:

$\frac{\sqrt{2}}{3}$

$\frac{1}{\sqrt{2}}$

$\frac{3}{\sqrt{2}}$

$\frac{2}{\sqrt{2}}$

None

24.

$\sin {2\theta}=$_______

$\frac{2 \tan{\theta}}{1+\tan^2 {\theta}}$

$\frac{1- \tan^2{\theta}}{1+\tan^2 {\theta}}$

$\frac{2 \tan{\theta}}{1-\tan^2 {\theta}}$

$\frac{\tan{\theta}}{1+\tan^2 {\theta}}$

None

25.

$\frac {1-\cos {x}}{\sin {x}}=$

$\cot {\frac{x}{2}}$

$-\cot {\frac{x}{2}}$

$-\tan {\frac{x}{2}}$

$\tan {\frac{x}{2}}$

None

26.

$\sin {22.5^{\circ}}\cos {22.5^{\circ}}+\cos {22.5^{\circ}}\sin {22.5^{\circ}}=$

$\frac{1}{\sqrt{2}}$

$\frac{-1}{\sqrt{2}}$

$\frac{-1}{\sqrt{3}}$

$\frac{1}{\sqrt{3}}$

None

27.

$\tan (\frac{\pi}{6}+\frac{\pi}{4})=$

$\frac {\sqrt{3} -1}{\sqrt{3} +1}$

$\frac {\sqrt{3} -1}{-\sqrt{3} +1}$

$\frac {\sqrt{3} +1}{\sqrt{3} -1}$

$\frac {\sqrt{3} +1}{-\sqrt{3} -1}$

None

28.

$\sin (45^{\circ} - 30^{\circ})=?$

$\frac {\sqrt {3} - \sqrt {2}}{2}$

$\frac {\sqrt {6} - \sqrt {2}}{4}$

$\frac {\sqrt {6} - \sqrt {2}}{2}$

$\frac {\sqrt {6} + \sqrt {2}}{4}$

None

29.

$\frac{1-\tan^2 {x}}{1+\tan^2 {x}}=?$

$\cot {2x}$

$\tan {2x}$

$\cos {2x}$

$\sin {2x}$

None

30.

If $\sin {\beta}= \frac {3}{5}$ then $\cos {2\beta}=$

$\frac {7}{25}$

$\frac {-7}{25}$

$\frac {7}{5}$

$\frac {-7}{5}$

None

31.

If $\alpha, \beta, \gamma$ are the angles of a triangle then $\tan (\alpha + \beta) + \tan {\gamma}$

non of these

None

32.

$\sin {\alpha}=\frac {2}{3}$, $\cos {\alpha}=\frac{3}{4}$, $\sin {2\alpha}=?$

$1$

$\frac {1}{3}$

$\frac {15}{144}$

$\frac {1}{2}$

None

33.

$\tan {\frac{\alpha}{2}}=$_______

$\pm \sqrt{\frac{1-\sin{\alpha}}{1+\sin{\alpha}}}$

$\pm \sqrt{\frac{1+\cos{\alpha}}{1-\cos{\alpha}}}$

$\pm \sqrt{\frac{1-\sin{\alpha}}{1-\cos{\alpha}}}$

$\pm \sqrt{\frac{1-\cos{\alpha}}{1+\cos{\alpha}}}$

None

34.

$\cos {48^\circ} +\cos {12^\circ}=?$

$\sqrt{3} \cos {18^\circ}$

$3\cos {18^\circ}$

$2\cos {18^\circ}$

$\sqrt{2} \cos {18^\circ}$

None

35.

$\sin {390^\circ}$ is equal to

$\sin {30^\circ}$

zero

$\cos {30^\circ}$

$\sin {60^\circ}$

None

36.

$\cos (\theta - 90^{\circ})-\cos (\theta + 90^{\circ})=$________

$-2\sin {\theta}$

$-2\cos {\theta}$

$2\sin {\theta}$

$2\cos {\theta}$

None

37.

$\frac{\sin {2\alpha} \cos {\alpha}}{\cos^3 {\alpha}-\cos {\alpha} \sin^2 {\alpha}}$

$\tan {2\alpha}$

$-\sec {\alpha}$

$\tan {\alpha}$

$\cos {\alpha}$

None

38.

$\tan (\frac {\pi}{2}+\theta)=?$

$\cot {\theta}$

$-\cot {\theta}$

$\tan {\theta}$

$-\tan {\theta}$

None

39.

$1+\cos{2\theta}$ is equal to ______

$2\cos {2\theta}$

$2\cos^2 {\theta}$

$2\sin {2\theta}$

$2\sin^2 {\theta}$

None

40.

If $\alpha, \beta$ and $\gamma$ are angles of triangle ABC, then $\cos(\frac{\alpha+\beta}{2})$ will be equal to _______.

$\sin {\beta}$

$\sin {\alpha}$

$\sin {\frac{\gamma}{2}}$

$\sin {\gamma}$

None

41.

$\cos {3\alpha}$ equal to:

$2\cos {\frac{3\alpha}{2}} \sin {\frac{3\alpha}{2}}$

$4 \cos^3 {\alpha}-3\cos {\alpha}$

$4 \sin^3 {\alpha}-4\sin {\alpha}$

$\cos^2 {\frac{3\alpha}{2}}-\sin^2 {\frac{3\alpha}{2}} $

None

42.

$\cos^2 {\theta}=?$

$\frac{\cos{2\theta}-1}{2}$

$\frac{1-\cos{2\theta}}{2}$

$\frac{1+\cos{2\theta}}{2}$

$\frac{1+\cos{\theta}}{2}$

None

43.

$\cos^2 {3x} - \sin^2 {3x}=$

$\sin {6x}$

$-\cos {6x}$

$\cos {6x}$

$-\sin {6x}$

None

44.

On simplifying the expansion $\frac{\sin {2\theta}}{1+\cos {2\theta}}$, the results is.

$\cot {\theta}$

$\sec {\theta}$

$\tan {\theta}$

$\sin {\theta}$

None

45.

$\cos {2\theta}=$_______

$2\cos^2 {\theta}+1$

$\frac{2 \tan{\theta}}{1+\tan^2 {\theta}}$

$\frac{2 \tan{\theta}}{1-\tan^2 {\theta}}$

$\frac{1- \tan^2{\theta}}{1+\tan^2 {\theta}}$

None

46.

$(\sin {x} - \cos {x})^2$

$1-\sin {2x}$

$1+\cos {2x}$

$1-\cos {2x}$

$1+\sin {2x}$

None

1 out of 46

Chapter 8: Fundamentals of Trigonometry – MCQs Preparation Test | National Book Foundation

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