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 7 of 23

1. Q121 CBSE 2026
   If $\sin x=p$, ​then ​prove that ​:

   1. (i)$\cot x=\frac{\sqrt{1-p^2}}{p}$
   2. (ii)$\frac{1+{\tan }^{2}x}{1+{\cot }^{2}x}=\frac{p^2}{1-p^2}$
   Show answer

   With $\sin x=p$, (i) $\cot x=\frac{\sqrt{1-p^2}}{p}$ and (ii) $\frac{1+{\tan }^{2}x}{1+{\cot }^{2}x}=\frac{p^2}{1-p^2}$ are both proved.

   Step-by-step solution →
2. Q122 CBSE 2026
   Prove ​that ​: $\frac{1+\mathrm{cosec}\theta }{\mathrm{cosec}\theta }=\frac{{\cos }^2\theta }{1-\sin \theta }$
   Show answer

   Both sides simplify to $1+\sin \theta$, so $\frac{1+\mathrm{cosec}\theta }{\mathrm{cosec}\theta }=\frac{{\cos }^2\theta }{1-\sin \theta }$ - proved.

   Step-by-step solution →
3. Q123 CBSE 2026
   If $\sin (A+2B)=1$ and $\cos (2A+B)=\frac{1}{2}$, find the values ​of $A$ and $B$. ​Hence, find ​the value ​of $\tan (B-A)$.
   Show answer

   $A=10^{\circ }$, $B=40^{\circ }$ and $\tan (B-A)=\tan 30^{\circ }=\frac{1}{\sqrt{3}}$.

   Step-by-step solution →
4. Q124 CBSE 2026
   If $\cos \theta +\sin \theta =\sqrt{2}\cos \theta$, then ​prove ​that $\cos \theta -\sin \theta =\sqrt{2}\sin \theta$.
   Show answer

   Both $\cos \theta -\sin \theta$ and $\sqrt{2}\sin \theta$ equal $(2-\sqrt{2})\cos \theta$, hence $\cos \theta -\sin \theta =\sqrt{2}\sin \theta$ is proved.

   Step-by-step solution →
5. Q125 CBSE 2026
   If $\cos A+\sin A=\sqrt{2}\cos A$, ​prove ​that $\cos A-\sin A=\sqrt{2}\sin A$.
   Show answer

   Squaring the given relation gives $2\sin A\cos A=2{\cos }^{2}A-1$; substituting into $(\cos A-\sin A{)}^2$ yields $2{\sin }^{2}A$, so $\cos A-\sin A=\sqrt{2}\sin A$. Hence proved.

   Step-by-step solution →
6. Q126 CBSE 2020
   If $\sin \theta +\cos \theta =\sqrt{3}$, ​then ​prove that $\tan \theta +\cot \theta =1$.
   Show answer

   Since $\sin \theta \cos \theta =1$, we get $\tan \theta +\cot \theta =\frac{1}{\sin \theta \cos \theta }=1$, as required.

   Step-by-step solution →
7. Q127 CBSE 2025
   If $7{\cos }^2\theta +3{\sin }^2\theta =4$, then ​the ​value ​of $\theta$ is ​:

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

   (c) $60^{\circ }$

   Step-by-step solution →
8. Q128 CBSE 2025
   If $\tan 3\theta =\sqrt{3}$, ​then $\frac{\theta }{2}$ ​equals :

   1. (a)$60^{\circ }$
   2. (b)$30^{\circ }$
   3. (c)$20^{\circ }$
   4. (d)$10^{\circ }$
   Show answer

   (d) $10^{\circ }$

   Step-by-step solution →
9. Q129 CBSE 2025
   If $\theta$ is an ​acute ​angle and $7+4\sin \theta =9$, ​then ​the value of $\theta$ ​is ​:

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

   (b) $30^{\circ }$

   Step-by-step solution →
10. Q130 CBSE 2025
    The ​value ​of ${\tan }^2\theta -\left(\frac{1}{\cos \theta }\times \sec \theta \right)$ ​is ​:

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

    (c) $-1$

    Step-by-step solution →
11. Q131 CBSE 2025
    If $\sqrt{2}\sin \theta =1$, ​then $\cot \theta \times \mathrm{cosec}\theta$ ​is ​equal ​to :

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

    (c) $\sqrt{2}$

    Step-by-step solution →
12. Q132 CBSE 2025
    The ​value ​of $\frac{1-{\tan }^{2}45^{\circ }}{1+{\tan }^{2}45^{\circ }}$ is ​equal ​to ​the value of ​:

    1. (a)$\tan 30^{\circ }$
    2. (b)$\tan 60^{\circ }$
    3. (c)$\tan 90^{\circ }$
    4. (d)$\tan 0^{\circ }$
    Show answer

    (d) $\tan 0^{\circ }$

    Step-by-step solution →
13. Q133 CBSE 2025
    $\tan 2A=3\tan A$ ​is ​true, ​when the measure of $\angle A$ ​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 →
14. Q134 CBSE 2025
    The ​value ​of $\frac{{\sec }^{2}30^{\circ }+{\tan }^{2}30^{\circ }}{{\sin }^{2}45^{\circ }+{\cos }^{2}45^{\circ }}$ is ​:

    1. (a)1
    2. (b)$\frac{5}{3}$
    3. (c)$\frac{13}{3}$
    4. (d)7
    Show answer

    (b) $\frac{5}{3}$

    Step-by-step solution →
15. Q135 CBSE 2025
    If $x=p{\cos }^3\alpha$ ​and $y=q{\sin }^3\alpha$, ​then ​the value ​of ${\left(\frac{x}{p}\right)}^{2/3}+{\left(\frac{y}{q}\right)}^{2/3}$ is ​:

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

    (a) 1

    Step-by-step solution →
16. Q136 CBSE 2025
    $(\cot \theta +\tan \theta )$ ​equals ​:

    1. (a)$\csc \theta \sec \theta$
    2. (b)$\sin \theta \sec \theta$
    3. (c)$\cos \theta \tan \theta$
    4. (d)$\sin \theta \cos \theta$
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    (a) $\csc \theta \sec \theta$

    Step-by-step solution →
17. Q137 CBSE 2025
    Which of ​the following ​statements ​is ​true?

    1. (a)$\sin 20^{\circ }>\sin 70^{\circ }$
    2. (b)$\sin 20^{\circ }>\cos 20^{\circ }$
    3. (c)$\cos 20^{\circ }>\cos 70^{\circ }$
    4. (d)$\tan 20^{\circ }>\tan 70^{\circ }$
    Show answer

    (c) $\cos 20^{\circ }>\cos 70^{\circ }$

    Step-by-step solution →
18. Q138 CBSE 2025
    Which ​of the ​following ​statements ​is false?

    1. (a)$\tan 45^{\circ }=\cot 45^{\circ }$
    2. (b)$\sin 90^{\circ }=\tan 45^{\circ }$
    3. (c)$\sin 30^{\circ }=\cos 30^{\circ }$
    4. (d)$\sin 45^{\circ }=\cos 45^{\circ }$
    Show answer

    (c) $\sin 30^{\circ }=\cos 30^{\circ }$

    Step-by-step solution →
19. Q139 CBSE 2025
    If $\sin \theta +\cos \theta =\sqrt{2}$, ​then $\tan \theta +\cot \theta$ is ​equal ​to:

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

    (d) $2$

    Step-by-step solution →
20. Q140 CBSE 2025
    The ​value of $\frac{2\tan 60^{\circ }}{1-{\tan }^{2}60^{\circ }}$ ​is ​:

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

    (d) $-\sqrt{3}$

    Step-by-step solution →