Class 10 Maths · Chapter 8

Introduction to Trigonometry

120 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 5 of 6

1. Q81 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 →
2. Q82 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 →
3. Q83 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 →
4. Q84 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 →
5. Q85 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 →
6. Q86 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 →
7. Q87 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 →
8. Q88 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 →
9. Q89 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 →
10. Q90 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 →
11. Q91 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 →
12. Q92 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 →
13. Q93 CBSE 2026
    If $\tan \theta +\frac{1}{\tan \theta }=2$, ​find the ​value ​of ${\tan }^2\theta +\frac{1}{{\tan }^2\theta }$.
    Show answer

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

    Step-by-step solution →
14. Q94 CBSE 2026
    Prove ​that: $\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=2\text{cosec}A$.
    Show answer

    Hence $\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=2\text{cosec}A$ is proved.

    Step-by-step solution →
15. Q95 CBSE 2026
    Evaluate ​: $\frac{{\sin }^{3}60^{\circ }-\tan 30^{\circ }}{{\cos }^{2}45^{\circ }}$
    Show answer

    $\frac{{\sin }^{3}60^{\circ }-\tan 30^{\circ }}{{\cos }^{2}45^{\circ }}=\frac{\sqrt{3}}{12}$.

    Step-by-step solution →
16. Q96 CBSE 2026
    If $7{\sin }^{2}A+3{\cos }^{2}A=4$, then ​find ​the ​value ​of $\tan A$.
    Show answer

    $\tan A=\frac{1}{\sqrt{3}}$ (equivalently $\frac{\sqrt{3}}{3}$), which corresponds to $A=30^{\circ }$.

    Step-by-step solution →
17. Q97 CBSE 2026
    Evaluate ​: ${\sin }^{2}30^{\circ }-{\cos }^{2}45^{\circ }+{\cot }^{2}60^{\circ }$
    Show answer

    ${\sin }^{2}30^{\circ }-{\cos }^{2}45^{\circ }+{\cot }^{2}60^{\circ }=\frac{1}{12}$

    Step-by-step solution →
18. Q98 CBSE 2026
    Triangle $ABC$ ​is an ​isosceles right ​triangle, ​right ​angled ​at $B$. Find ​the value ​of ${\sin }^{2}A+{\cos }^{2}C$.
    Show answer

    ${\sin }^{2}A+{\cos }^{2}C=1$

    Step-by-step solution →
19. Q99 CBSE 2026
    In the given figure, $△MEN$ is ​a ​right triangle, right-angled at $E$. If $\angle EMN=60^{\circ }$ and $ME=5$ cm, ​find the length of $MN$. ​Also, ​find the ​value ​of ${\sin }^{2}N$.

    Show answer

    $MN=10$ cm and ${\sin }^{2}N=\frac{1}{4}$

    Step-by-step solution →
20. Q100 CBSE 2026
    If $\cot \theta =\frac{7}{8}$, ​then find ​the value ​of $\frac{(1+\sin \theta )(1-\sin \theta )}{(1+\cos \theta )(1-\cos \theta )}$.
    Show answer

    The value of the expression is $\frac{49}{64}$.

    Step-by-step solution →