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 15 of 23

1. Q281 CBSE 2024
   If $\cos A=\frac{5}{13}$, ​then ​verify that $\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-\cot A}=\cos A+\sin A$.
   Show answer

   With $\sin A=\frac{12}{13}$, $\tan A=\frac{12}{5}$ and $\cot A=\frac{5}{12}$: LHS $=-\frac{25}{91}+\frac{144}{91}=\frac{17}{13}$ and RHS $=\frac{5}{13}+\frac{12}{13}=\frac{17}{13}$. Both sides equal $\frac{17}{13}$, so the result is verified.

   Step-by-step solution →
2. Q282 CBSE 2023
   If $2\cos \theta =1$, ​then ​the value of $\theta$ ​is

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

   (b) $60^{\circ }$

   Step-by-step solution →
3. Q283 CBSE 2023
   If $\mathrm{cosec}A=\frac{7}{5}$, ​then value ​of $\tan A\times \cos A$ ​is:

   1. (a)$\frac{7}{5}$
   2. (b)$\frac{2\sqrt{6}}{5}$
   3. (c)$\frac{24}{49}$
   4. (d)$\frac{5}{7}$
   Show answer

   (d) $\frac{5}{7}$

   Step-by-step solution →
4. Q284 CBSE 2023
   $9{\sec }^{2}A-9{\tan }^{2}A$ is ​equal ​to ​:

   1. (a)$9$
   2. (b)$0$
   3. (c)$8$
   4. (d)$\frac{1}{9}$
   Show answer

   (a) $9$

   Step-by-step solution →
5. Q285 CBSE 2023
   In $△ABC$, right ​angled at $C$, ​if $\tan A=\frac{8}{7}$, then ​the value ​of $\cot B$ ​is

   1. (a)$\frac{7}{8}$
   2. (b)$\frac{8}{7}$
   3. (c)$\frac{7}{\sqrt{113}}$
   4. (d)$\frac{8}{\sqrt{113}}$
   Show answer

   (b) $\frac{8}{7}$

   Step-by-step solution →
6. Q286 CBSE 2023
   If $2\tan A=3$, ​then the ​value ​of $\frac{4\sin A+3\cos A}{4\sin A-3\cos A}$ ​is

   1. (a)$\frac{7}{\sqrt{13}}$
   2. (b)$\frac{1}{\sqrt{13}}$
   3. (c)3
   4. (d)does not exist
   Show answer

   (c) 3

   Step-by-step solution →
7. Q287 CBSE 2023
   If $\tan \theta =\frac{5}{12}$, ​then ​the ​value ​of $\frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }$ is :

   1. (a)$-\frac{17}{7}$
   2. (b)$\frac{17}{7}$
   3. (c)$\frac{17}{13}$
   4. (d)$-\frac{7}{13}$
   Show answer

   (a) $-\frac{17}{7}$

   Step-by-step solution →
8. Q288 CBSE 2023
   ${\cot }^2\theta -\frac{1}{{\sin }^2\theta }$ is ​equal ​to ​:

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

   (d) -1

   Step-by-step solution →
9. Q289 CBSE 2023
   If $x=a\sin \theta$ ​and $y=b\cos \theta$, ​then $b^2{x}^2+a^2{y}^2$ ​is ​equal to:

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

   (b) $a^2{b}^2$

   Step-by-step solution →
10. Q290 CBSE 2023
    $\frac{{\cos }^2\theta }{{\sin }^2\theta }-\frac{1}{{\sin }^2\theta }$, in ​simplified ​form, ​is ​:

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

    (d) $-1$

    Step-by-step solution →
11. Q291 CBSE 2023
    $\left[\frac{3}{4}{\tan }^{2}30^{\circ }-{\sec }^{2}45^{\circ }+{\sin }^{2}60^{\circ }\right]$ ​is ​equal ​to

    1. (a)$-1$
    2. (b)$\frac{5}{6}$
    3. (c)$\frac{-3}{2}$
    4. (d)$\frac{1}{6}$
    Show answer

    (a) $-1$

    Step-by-step solution →
12. Q292 CBSE 2023
    The ​value ​of $5{\sin }^{2}90^{\circ }-2{\cos }^2{0}^{\circ }$ is ​:

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

    (c) $3$

    Step-by-step solution →
13. Q293 CBSE 2023
    $\sec \theta$ when ​expressed in terms of $\cot \theta$, ​is ​equal to ​:

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

    (c) $\frac{\sqrt{1+{\cot }^2\theta }}{\cot \theta }$

    Step-by-step solution →
14. Q294 CBSE 2023
    If $\sin \theta =\frac{a}{b}$, ​then $\sec \theta$ ​is equal ​to $(0\le \theta \le 90^{\circ })$ ​:

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

    Step-by-step solution →
15. Q295 CBSE 2023
    If $\tan A=\frac{3}{4}$, ​then ​the value of $\frac{4\sin A-2\cos A}{4\sin A+2\cos A}$ ​is:

    1. (a)$5$
    2. (b)$\frac{1}{5}$
    3. (c)$6$
    4. (d)$\frac{1}{6}$
    Show answer

    (b) $\frac{1}{5}$

    Step-by-step solution →
16. Q296 CBSE 2023
    If $\sqrt{3}\tan 2\theta =3$, $0^{\circ }<2\theta <90^{\circ }$, then ​the ​value of $\sin \theta +\sqrt{3}\cos \theta$ is ​:

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

    (a) $2$

    Step-by-step solution →
17. Q297 CBSE 2023
    $\left(\frac{2\tan 30^{\circ }}{1+{\tan }^{2}30^{\circ }}\right)$ ​is equal ​to ​:

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

    (a) $\sin 60^{\circ }$

    Step-by-step solution →
18. Q298 CBSE 2023
    If $\tan \theta =\frac{3}{4}$, then ​the ​value ​of $\cos \theta$ is ​:

    1. (a)$\frac{3}{5}$
    2. (b)$\frac{4}{5}$
    3. (c)$\frac{3}{7}$
    4. (d)$\frac{4}{7}$
    Show answer

    (b) $\frac{4}{5}$

    Step-by-step solution →
19. Q299 CBSE 2023
    If $2\sin 2A=\sqrt{3}$, ​then $\angle A$ ​is equal to:

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

    (d) $30^{\circ }$

    Step-by-step solution →
20. Q300 CBSE 2023
    If $\cos \theta +\sin \theta =\sqrt{2}\cos \theta$, ​then $\cos \theta -\sin \theta$ ​equals :

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

    (b) $\sqrt{2}\sin \theta$

    Step-by-step solution →