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 8 of 23

1. Q141 CBSE 2025
   The value ​of $\left({\tan }^{2}A-\frac{1}{{\cos }^{2}A}\right)$ ​is ​:

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

   (d) $-1$

   Step-by-step solution →
2. Q142 CBSE 2025
   If $\sin \theta -\cos \theta =0$, then the ​value of ${\sin }^6\theta +{\cos }^6\theta$ ​is

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

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

   Step-by-step solution →
3. Q143 CBSE 2025
   The ​value ​of $({\sin }^{2}A+{\cos }^{2}A)+({\sec }^{2}A-{\tan }^{2}A)-({\cot }^{2}A-{\csc }^{2}A)$ is :

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

   (c) 3

   Step-by-step solution →
4. Q144 CBSE 2025
   If $\sec \theta -\tan \theta =2$, ​then $\sec \theta +\tan \theta$ ​is ​equal to :

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

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

   Step-by-step solution →
5. Q145 CBSE 2025
   If $4\tan A=3$, ​then $\frac{4\sin A-\cos A}{4\sin A+\cos A}$ is equal ​to:

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

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6. Q146 CBSE 2025
   If $\sin \theta +\cos \theta =\sqrt{2}\cos \theta ,(\theta \ne 90^{\circ })$, then $\tan \theta$ ​is equal ​to

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

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

   Step-by-step solution →
7. Q147 CBSE 2025
   If $x\left(\frac{2\tan 30^{\circ }}{1+{\tan }^{2}30^{\circ }}\right)=y\left(\frac{2\tan 30^{\circ }}{1-{\tan }^{2}30^{\circ }}\right)$, ​then $x:y=$

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

   (c) $2:1$

   Step-by-step solution →
8. Q148 CBSE 2025
   $\frac{1-{\tan }^{2}30^{\circ }}{1+{\tan }^{2}30^{\circ }}$ is ​equal ​to

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

   (b) $\cos 60^{\circ }$

   Step-by-step solution →
9. Q149 CBSE 2025
   If $\tan A=1$, ​then $3\sin A+\cos A$ ​is ​equal to

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

   (c) $2\sqrt{2}$

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10. Q150 CBSE 2025
    If $\sin 30^{\circ }\tan 45^{\circ }=\frac{\sec 60^{\circ }}{k}$, then ​the ​value ​of $k$ ​is :

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

    Step-by-step solution →
11. Q151 CBSE 2025
    Find ​the value ​of $\frac{\tan \alpha }{\tan \beta }$ from ​the following ​diagram. It ​is given ​that $RS:SQ=1:2$.

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

    (c) 3

    Step-by-step solution →
12. Q152 CBSE 2025
    If $\sqrt{3}\sin \theta =\cos \theta$, ​then the ​value of $\theta$ ​is

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

    (d) $30^{\circ }$

    Step-by-step solution →
13. Q153 CBSE 2025
    If $\sin \theta +{\sin }^2\theta =1$, ​then the ​value ​of ${\cos }^2\theta +{\cos }^4\theta$ is:

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

    Step-by-step solution →
14. Q154 CBSE 2025
    If $\sin A=\frac{2}{3}$, ​then $\cos A$ is equal to ​:

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

    Step-by-step solution →
15. Q155 CBSE 2025
    If $△ABC$ ​is ​right-angled at $C$, then ​the ​value of $\cos (A+B)$ ​is:

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

    Step-by-step solution →
16. Q156 CBSE 2025
    In $△ABC$, $\angle B=90^{\circ }$. ​If $\frac{AB}{AC}=\frac{1}{2}$, then $\cos C$ ​is ​equal ​to

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

    Step-by-step solution →
17. Q157 CBSE 2025
    In ​a right ​triangle $ABC$, right-angled at $A$, ​if $\sin B=\frac{1}{4}$, then ​the ​value of $\sec B$ is

    1. (a)$4$
    2. (b)$\frac{\sqrt{15}}{4}$
    3. (c)$\sqrt{15}$
    4. (d)$\frac{4}{\sqrt{15}}$
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    (d) $\frac{4}{\sqrt{15}}$

    Step-by-step solution →
18. Q158 CBSE 2025
    If $x\tan 45^{\circ }\cos 60^{\circ }=\sqrt{3}\sin 60^{\circ }\cot 60^{\circ }$, then ​the value ​of $x$ ​is ​:

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

    (c) $\sqrt{3}$

    Step-by-step solution →
19. Q159 CBSE 2025
    Direction: ​In the following question, ​an Assertion (A) and a Reason ​(R) ​are given. ​Choose the correct option. Assertion ​(A) : ​For $\sin \theta =1$, $\cos \theta$ must ​be $0$. Reason (R) : ${\sin }^2\theta -{\cos }^2\theta =1.$

    Assertion (A): For $\sin \theta =1$, $\cos \theta$ must be $0$.

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

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

    Step-by-step solution →
20. Q160 CBSE 2025
    Choose ​the correct option (a)-(d) ​based ​on the truth values ​of the Assertion (A) ​and ​Reason (R) ​below.

    Assertion (A): For an acute angle $\theta$, $\sin \theta =\frac{3}{5}\Rightarrow \cos \theta =-\frac{4}{5}$.

    Reason (R): For any value of $\theta$, $(0^{\circ }\le \theta \le 90^{\circ })$, ${\sin }^2\theta +{\cos }^2\theta =1$.

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

    (d) A is false but R is true.

    Step-by-step solution →