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 16 of 23

1. Q301 CBSE 2023
   If $2\sin A=\mathrm{cosec}A$, ​then $\angle A$ ​is ​equal to ​:

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

   (c) $45^{\circ }$

   Step-by-step solution →
2. Q302 CBSE 2023
   If $\cos A=\frac{\sqrt{3}}{2}$, ​then the ​value ​of $\cot A$ is ​:

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

   (a) $\sqrt{3}$

   Step-by-step solution →
3. Q303 CBSE 2023
   If $\tan (A+B)=\sqrt{3}$ and $\tan (A-B)=\frac{1}{\sqrt{3}}$, $0^{\circ }<A+B<90^{\circ }$, $A>B$, then the ​values of A ​and ​B ​respectively ​are ​:

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

   (c) $45^{\circ },15^{\circ }$

   Step-by-step solution →
4. Q304 CBSE 2023
   If $\cot \theta +\tan \theta =1$, then ​the ​value ​of ${\cot }^2\theta +{\tan }^2\theta$ is :

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

   (b) $-1$

   Step-by-step solution →
5. Q305 CBSE 2023
   The value of $2{\sin }^{2}30^{\circ }+3{\tan }^{2}60^{\circ }-{\cos }^{2}45^{\circ }$ ​is ​:

   1. (a)$3\sqrt{3}$
   2. (b)$\frac{19}{2}$
   3. (c)$\frac{9}{4}$
   4. (d)$9$
   Show answer

   (d) $9$

   Step-by-step solution →
6. Q306 CBSE 2023
   If $\theta$ is an ​acute ​angle of ​a right ​angled triangle, then which ​of ​the ​following equation is **not** true?

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

   (d) ${\tan }^2\theta -{\sec }^2\theta =1$

   Step-by-step solution →
7. Q307 CBSE 2023
   If $\sin \theta =\frac{3}{4}$, then $\frac{({\sec }^2\theta -1){\cos }^2\theta }{\sin \theta }$ equals ​:

   1. (a)$\frac{3}{5}$
   2. (b)$\frac{3}{4}$
   3. (c)$\frac{4}{3}$
   4. (d)$\frac{9}{16}$
   Show answer

   (b) $\frac{3}{4}$

   Step-by-step solution →
8. Q308 CBSE 2023
   If $\tan A=\frac{2}{5}$, ​then the ​value of $\frac{1-{\cos }^{2}A}{1-{\sin }^{2}A}$ ​is :

   1. (a)$\frac{25}{4}$
   2. (b)$\frac{4}{25}$
   3. (c)$\frac{4}{5}$
   4. (d)$\frac{5}{4}$
   Show answer

   (b) $\frac{4}{25}$

   Step-by-step solution →
9. Q309 CBSE 2023
   Assertion (A): For $0<\theta \le 90^{\circ }$, $\mathrm{cosec}\theta -\cot \theta$ and $\mathrm{cosec}\theta +\cot \theta$ are reciprocal of each other.

   Reason (R): ${\mathrm{cosec}}^2\theta -{\cot }^2\theta =1$

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true, but Reason (R) is false.
   4. (d)Assertion (A) is false, but Reason (R) is true.
   Show answer

   (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

   Step-by-step solution →
10. Q310 CBSE 2023
    Assertion-Reason ​type question. ​Choose ​the correct option ​about the Assertion (A) ​and ​the Reason (R) ​given below.

    Assertion (A): For $0<\theta \le 90^{\circ }$, $\csc \theta -\cot \theta$ and $\csc \theta +\cot \theta$ are reciprocal of each other.

    Reason (R): ${\cot }^2\theta -{\csc }^2\theta =1$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (c) Assertion (A) is true, but Reason (R) is false.

    Step-by-step solution →
11. Q311 CBSE 2023
    If $\sin \alpha =\frac{1}{2}$, ​then find ​the ​value ​of $(3\cos \alpha -4{\cos }^3\alpha )$.
    Show answer

    $0$

    Step-by-step solution →
12. Q312 CBSE 2023
    Evaluate ​: $5{\csc }^{2}45^{\circ }-3{\sin }^{2}90^{\circ }+5\cos 0^{\circ }$.
    Show answer

    $12$

    Step-by-step solution →
13. Q313 CBSE 2023
    Evaluate: ${\tan }^{2}60^{\circ }-2{\csc }^{2}30^{\circ }-2{\tan }^{2}30^{\circ }$.
    Show answer

    $-\frac{17}{3}$

    Step-by-step solution →
14. Q314 CBSE 2023
    If $4{\cot }^{2}45^{\circ }-{\sec }^{2}60^{\circ }+{\sin }^{2}60^{\circ }+p=\frac{3}{4}$, ​then ​find ​the ​value ​of $p$.
    Show answer

    $p=0$

    Step-by-step solution →
15. Q315 CBSE 2023
    Evaluate ​: $\frac{\sin 30^{\circ }+\tan 45^{\circ }}{\sec 30^{\circ }+\cot 45^{\circ }}$
    Show answer

    $\frac{6\sqrt{3}-9}{2}$

    Step-by-step solution →
16. Q316 CBSE 2023
    For $A=30^{\circ }$ and $B=60^{\circ }$, verify ​that ​: $\sin (A+B)=\sin A\cos B+\cos A\sin B.$
    Show answer

    Both sides equal 1, so the identity is verified.

    Step-by-step solution →
17. Q317 CBSE 2023
    If $\cos A+{\cos }^{2}A=1$, ​then ​find the ​value ​of ${\sin }^{2}A+{\sin }^{4}A$.
    Show answer

    ${\sin }^{2}A+{\sin }^{4}A=1$

    Step-by-step solution →
18. Q318 CBSE 2023
    If $\sin \theta +\cos \theta =\sqrt{3}$, ​then ​find ​the value ​of $\sin \theta \times \cos \theta$.
    Show answer

    $\sin \theta \cos \theta =1$

    Step-by-step solution →
19. Q319 CBSE 2023
    If $\sin \alpha =\frac{1}{\sqrt{2}}$ and $\cot \beta =\sqrt{3}$, then find ​the ​value ​of $\csc \alpha +\csc \beta$.
    Show answer

    $\csc \alpha +\csc \beta =\sqrt{2}+2$

    Step-by-step solution →
20. Q320 CBSE 2023
    If $\tan A=1$ and $\tan B=\sqrt{3}$, then ​evaluate $\cos A\cos B+\sin A\sin B$.
    Show answer

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

    Step-by-step solution →