Class 10 Maths · Chapter 8

Introduction to Trigonometry

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

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 4 of 6

1. Q61 CBSE 2026
   If $\sin \theta =\frac{\sqrt{3}}{2}$, ​then ​the ​value of $2\sqrt{3}\cdot \cos \frac{\theta }{2}$ is:

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

   (a) $3$

   Step-by-step solution →
2. Q62 CBSE 2026
   The value ​of $\sin 90^{\circ }\cos 90^{\circ }-{\sin }^{2}60^{\circ }$ ​is:

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

   (c) $-\frac{3}{4}$

   Step-by-step solution →
3. Q63 CBSE 2026
   Which ​of ​the ​following statements ​is ​not true ​?

   1. (a)$\sin 0^{\circ }=\cos 0^{\circ }$
   2. (b)$\tan 30^{\circ }=\cot 60^{\circ }$
   3. (c)$\sin 30^{\circ }=\cos 60^{\circ }$
   4. (d)$\sin 45^{\circ }=\frac{1}{\sec 45^{\circ }}$
   Show answer

   (a) $\sin 0^{\circ }=\cos 0^{\circ }$

   Step-by-step solution →
4. Q64 CBSE 2026
   One of ​the ​possible values of $A$, ​for which $\cos 2A=\cos A$, ​is :

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

   (a) $0^{\circ }$

   Step-by-step solution →
5. Q65 CBSE 2026
   Which of ​the ​following ​is ​not defined ​for $x=90^{\circ }$ ?

   1. (a)$\cot x$
   2. (b)$\text{cosec}x$
   3. (c)$\tan \left(\frac{x}{2}\right)$
   4. (d)$\sec x$
   Show answer

   (d) $\sec x$

   Step-by-step solution →
6. Q66 CBSE 2026
   For an acute ​angle $\theta$, ​if $\sin \theta =\frac{1}{9}$, ​then value ​of $\frac{9\mathrm{cosec}\theta +1}{9\mathrm{cosec}\theta -1}$ ​is

   1. (a)$0$
   2. (b)$\frac{80}{81}$
   3. (c)$1$
   4. (d)$\frac{82}{80}$
   Show answer

   (d) $\frac{82}{80}$

   Step-by-step solution →
7. Q67 CBSE 2026
   If $\sqrt{3}\sin A=\cos A$, ​then ​the ​measure of $A$ ​is ​:

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

   (d) $30^{\circ }$

   Step-by-step solution →
8. Q68 CBSE 2026
   Given that $\sin 2\alpha =\frac{\sqrt{3}}{2}$, ​the ​value ​of $\sin 3\alpha$ is ​:

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

   (c) $1$

   Step-by-step solution →
9. Q69 CBSE 2026
   If $\sin \theta =\frac{1}{7}$, then $\tan \theta$ ​is ​:

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

   (a) $\frac{1}{4\sqrt{3}}$

   Step-by-step solution →
10. Q70 CBSE 2026
    The ​value ​of $\left(\frac{1}{2}{\tan }^{2}45^{\circ }-{\cos }^{2}60^{\circ }\right)$ is ​:

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

    (c) $\frac{1}{4}$

    Step-by-step solution →
11. Q71 CBSE 2026
    Simplest form ​of $\frac{\sec A}{\sqrt{{\sec }^{2}A-1}}$ ​is

    1. (a)$\sin A$
    2. (b)$\tan A$
    3. (c)$\text{cosec}A$
    4. (d)$\cos A$
    Show answer

    (c) $\text{cosec}A$

    Step-by-step solution →
12. Q72 CBSE 2026
    $\sin 2\theta =2\sin \theta$ is ​true, ​when $\theta$ is ​equal ​to

    1. (a)$90^{\circ }$
    2. (b)$60^{\circ }$
    3. (c)$45^{\circ }$
    4. (d)$0^{\circ }$
    Show answer

    (d) $0^{\circ }$

    Step-by-step solution →
13. Q73 CBSE 2026
    In ​the following ​question, a statement ​of Assertion (A) is followed ​by a statement ​of ​Reason (R). Choose ​the correct option.

    Assertion (A): For an acute angle $\theta$, $\cos \theta$ is always less than $1$.

    Reason (R): In a right-angled triangle, the hypotenuse is the longest side and $\cos \theta =\frac{\text{Base}}{\text{Hypotenuse}}$.

    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 →
14. Q74 CBSE 2026
    In ​the question, a ​statement of ​Assertion ​(A) ​is followed by a statement ​of Reason (R). Choose the correct option.

    Assertion (A): $\tan 2\theta$ is not defined at $\theta =45^{\circ }$.

    Reason (R): $\sin 90^{\circ }\ne \cos 90^{\circ }$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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

    (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

    Step-by-step solution →
15. Q75 CBSE 2026
    If $\sin (A-B)=\frac{1}{2}$ and $\tan (A+B)=\sqrt{3}$, where $0^{\circ }\le A+B<90^{\circ }$ ​and $A>B$, then ​find the ​values of $A$ ​and $B$.
    Show answer

    $A=45^{\circ }$ and $B=15^{\circ }$.

    Step-by-step solution →
16. Q76 CBSE 2026
    If $\sec A=\sqrt{2}$ ​and $\tan B=\sqrt{3}$, ​then ​find ​the value of $2\sin A\cos B$.
    Show answer

    $2\sin A\cos B=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\approx 0.71$.

    Step-by-step solution →
17. Q77 CBSE 2026
    Evaluate ​: $\frac{4{\cos }^{3}60^{\circ }+\mathrm{cosec}30^{\circ }}{{\tan }^{2}30^{\circ }}$
    Show answer

    The value of the expression is $\frac{15}{2}$ (that is, $7.5$).

    Step-by-step solution →
18. Q78 CBSE 2026
    Prove ​that ​: $\sqrt{\frac{1+\sin A}{1-\sin A}}=\sec A+\tan A$.
    Show answer

    Proved: $\sqrt{\frac{1+\sin A}{1-\sin A}}=\frac{1+\sin A}{\cos A}=\sec A+\tan A$ (for $A$ acute).

    Step-by-step solution →
19. Q79 CBSE 2026
    Evaluate ​: $\frac{3{\cos }^{2}30^{\circ }-6{\mathrm{cosec}}^{2}30^{\circ }}{{\tan }^{2}60^{\circ }}$
    Show answer

    $\frac{3{\cos }^{2}30^{\circ }-6{\mathrm{cosec}}^{2}30^{\circ }}{{\tan }^{2}60^{\circ }}=-\frac{29}{4}$

    Step-by-step solution →
20. Q80 CBSE 2026
    If $\tan \theta =\frac{24}{7}$, ​then ​find ​the value of $\sin \theta +\cos \theta$.
    Show answer

    The value of $\sin \theta +\cos \theta$ is $\frac{31}{25}$.

    Step-by-step solution →