Class 10 Maths · Chapter 8

Introduction to Trigonometry

454 Class 10 Maths questions on Introduction to Trigonometry from the NCERT textbook, NCERT Exemplar and CBSE board papers 2018–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 12 of 23

1. Q221 CBSE 2024
   If $\cos \theta =\frac{\sqrt{3}}{2}$ and $\sin \varphi =\frac{1}{2}$, ​then $\tan (\theta +\varphi )$ is :

   1. (a)$\sqrt{3}$
   2. (b)$\frac{1}{\sqrt{3}}$
   3. (c)$1$
   4. (d)not defined
   Show answer

   (a) $\sqrt{3}$

   Step-by-step solution →
2. Q222 CBSE 2024
   $\frac{2\tan 30^{\circ }}{1-{\tan }^{2}30^{\circ }}$ ​is ​equal ​to

   1. (a)$\cos 60^{\circ }$
   2. (b)$\sin 60^{\circ }$
   3. (c)$\tan 60^{\circ }$
   4. (d)$\sin 30^{\circ }$
   Show answer

   (c) $\tan 60^{\circ }$

   Step-by-step solution →
3. Q223 CBSE 2024
   The ​value ​of $\left({\sin }^2\theta +\frac{1}{1+{\tan }^2\theta }\right)$ ​is :

   1. (a)$0$
   2. (b)$2$
   3. (c)$1$
   4. (d)$-1$
   Show answer

   (c) $1$

   Step-by-step solution →
4. Q224 CBSE 2024
   For ​what value of $\theta$, ${\sin }^2\theta +\sin \theta +{\cos }^2\theta$ ​is ​equal ​to $2$?

   1. (a)$45^{\circ }$
   2. (b)$0^{\circ }$
   3. (c)$90^{\circ }$
   4. (d)$30^{\circ }$
   Show answer

   (c) $90^{\circ }$

   Step-by-step solution →
5. Q225 CBSE 2024
   If $\sin \theta =1$, ​then the ​value ​of $\frac{1}{2}\sin \left(\frac{\theta }{2}\right)$ ​is :

   1. (a)$\frac{1}{2\sqrt{2}}$
   2. (b)$\frac{1}{\sqrt{2}}$
   3. (c)$\frac{1}{2}$
   4. (d)0
   Show answer

   (a) $\frac{1}{2\sqrt{2}}$

   Step-by-step solution →
6. Q226 CBSE 2024
   $\left(\frac{5}{{\cot }^2\theta }-\frac{5}{{\cos }^2\theta }\right)$ ​is equal ​to ​:

   1. (a)1
   2. (b)5
   3. (c)-5
   4. (d)0
   Show answer

   (c) -5

   Step-by-step solution →
7. Q227 CBSE 2024
   If $\tan A=3\cot A$, then the measure ​of the ​angle ​A ​is :

   1. (a)$15^{\circ }$
   2. (b)$30^{\circ }$
   3. (c)$45^{\circ }$
   4. (d)$60^{\circ }$
   Show answer

   (d) $60^{\circ }$

   Step-by-step solution →
8. Q228 CBSE 2024
   $\left(\frac{1}{{\tan }^2\theta }-\frac{1}{{\sin }^2\theta }\right)$ ​is ​equal ​to ​:

   1. (a)1
   2. (b)$-1$
   3. (c)${\sec }^2\theta$
   4. (d)${\sin }^2\theta$
   Show answer

   (b) $-1$

   Step-by-step solution →
9. Q229 CBSE 2024
   If ${\tan }^2\theta =3$, ​where $\theta$ is ​an ​acute ​angle, ​then ​the value of $\theta$ is ​:

   1. (a)30 degrees
   2. (b)60 degrees
   3. (c)0 degrees
   4. (d)45 degrees
   Show answer

   (b) 60 degrees

   Step-by-step solution →
10. Q230 CBSE 2024
    $(\sec \theta +\tan \theta )(1-\sin \theta )$ ​is ​equal ​to ​:

    1. (a)$\sec \theta$
    2. (b)$\sin \theta$
    3. (c)$\mathrm{cosec}\theta$
    4. (d)$\cos \theta$
    Show answer

    (d) $\cos \theta$

    Step-by-step solution →
11. Q231 CBSE 2024
    If $\mathrm{cosec}\theta =\sqrt{10}$, ​then ​the ​value ​of $\sec \theta$ is:

    1. (a)$\frac{3}{\sqrt{10}}$
    2. (b)$\frac{\sqrt{10}}{3}$
    3. (c)$\frac{1}{\sqrt{10}}$
    4. (d)$\frac{2}{\sqrt{10}}$
    Show answer

    (b) $\frac{\sqrt{10}}{3}$

    Step-by-step solution →
12. Q232 CBSE 2024
    If $\cos \theta =\frac{p}{q}$, then $\sin \theta$ ​is ​equal ​to ​:

    1. (a)$\frac{q}{\sqrt{q^2-p^2}}$
    2. (b)$\frac{q}{p}$
    3. (c)$\frac{\sqrt{q^2-p^2}}{q}$
    4. (d)$\frac{p}{\sqrt{q^2-p^2}}$
    Show answer

    (c) $\frac{\sqrt{q^2-p^2}}{q}$

    Step-by-step solution →
13. Q233 CBSE 2024
    If $\cos (\alpha +\beta )=0$, ​then value ​of $\cos \left(\frac{\alpha +\beta }{2}\right)$ is ​equal ​to :

    1. (a)$\frac{1}{\sqrt{2}}$
    2. (b)$\frac{1}{2}$
    3. (c)$0$
    4. (d)$\sqrt{2}$
    Show answer

    (a) $\frac{1}{\sqrt{2}}$

    Step-by-step solution →
14. Q234 CBSE 2024
    The maximum value ​of $\frac{1}{\mathrm{cosec}\theta }$, $(0\le \theta \le 90^{\circ })$ is:

    1. (a)$\frac{\sqrt{3}}{2}$
    2. (b)$1$
    3. (c)$\frac{1}{\sqrt{2}}$
    4. (d)$\sqrt{2}$
    Show answer

    (b) $1$

    Step-by-step solution →
15. Q235 CBSE 2024
    $\frac{{\sin }^{3}A+{\cos }^{3}A}{\sin A+\cos A}+\sin A\cos A$ ​on ​simplification ​gives:

    1. (a)$1$
    2. (b)$2$
    3. (c)$1+2\sin A\cos A$
    4. (d)$0$
    Show answer

    (a) $1$

    Step-by-step solution →
16. Q236 CBSE 2024
    The ​value ​of $\cos 60^{\circ }-\mathrm{cosec}30^{\circ }+\tan 45^{\circ }$ ​is ​:

    1. (a)$1$
    2. (b)$-\frac{1}{2}$
    3. (c)$\frac{1}{2}$
    4. (d)$-1$
    Show answer

    (b) $-\frac{1}{2}$

    Step-by-step solution →
17. Q237 CBSE 2024
    If $\mathrm{cosec}B=\frac{2}{\sqrt{3}}$ ​and $A+B=90^{\circ }$, ​then ​the ​value of $\sec A$ ​is:

    1. (a)$\frac{2}{\sqrt{3}}$
    2. (b)$\sqrt{2}$
    3. (c)$\frac{\sqrt{3}}{2}$
    4. (d)$2$
    Show answer

    (a) $\frac{2}{\sqrt{3}}$

    Step-by-step solution →
18. Q238 CBSE 2024
    If ${\tan }^2\theta +{\cot }^2\alpha =2$, where $\theta =45^{\circ }$ ​and $0^{\circ }\le \alpha \le 90^{\circ }$, then ​the ​value ​of $\alpha$ is ​:

    1. (a)$30^{\circ }$
    2. (b)$45^{\circ }$
    3. (c)$60^{\circ }$
    4. (d)$90^{\circ }$
    Show answer

    (b) $45^{\circ }$

    Step-by-step solution →
19. Q239 CBSE 2024
    If $\cos A=\frac{1}{2}$, ​then $\tan A$ ​is ​equal to

    1. (a)$\frac{1}{\sqrt{3}}$
    2. (b)$\sqrt{3}$
    3. (c)$3$
    4. (d)$\frac{3}{2}$
    Show answer

    (b) $\sqrt{3}$

    Step-by-step solution →
20. Q240 CBSE 2024
    The expression ${\sec }^4\theta -{\sec }^2\theta$ ​is ​equal to ​:

    1. (a)${\tan }^2\theta -{\tan }^4\theta$
    2. (b)$-{\tan }^4\theta -{\tan }^2\theta$
    3. (c)${\tan }^2\theta +{\tan }^4\theta$
    4. (d)${\tan }^4\theta -{\tan }^2\theta$
    Show answer

    (c) ${\tan }^2\theta +{\tan }^4\theta$

    Step-by-step solution →