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 3 of 6

1. Q41 Exemplar · Exercise 8.3
   If $\tan A=\frac{3}{4}$, ​then $\sin A\cos A=\frac{12}{25}$.
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   True

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2. Q42 Exemplar · Exercise 8.3
   Prove ​that $(\sin \alpha +\cos \alpha )(\tan \alpha +\cot \alpha )=\sec \alpha +\csc \alpha$.
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   LHS $=\sec \alpha +\csc \alpha =$ RHS (proved).

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3. Q43 Exemplar · Exercise 8.3
   Prove ​that $\left(\sqrt{3}+1\right)(3-\cot 30^{\circ })={\tan }^{3}60^{\circ }-2\sin 60^{\circ }$.
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   Both sides equal $2\sqrt{3}$, so the identity is proved.

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4. Q44 Exemplar · Exercise 8.3
   Prove ​that $1+\frac{{\cot }^2\alpha }{1+\csc \alpha }=\csc \alpha$.
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   The left side simplifies to $\csc \alpha$, equal to the right side, so the identity is proved.

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5. Q45 Exemplar · Exercise 8.3
   Prove ​that $\tan \theta +\tan (90^{\circ }-\theta )=\sec \theta \sec (90^{\circ }-\theta )$.
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   Proved: $\tan \theta +\tan (90^{\circ }-\theta )=\frac{1}{\sin \theta \cos \theta }=\sec \theta \sec (90^{\circ }-\theta )$.

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6. Q46 Exemplar · Exercise 8.3
   If $\sqrt{3}\tan \theta =1$, ​then find the ​value ​of ${\sin }^2\theta -{\cos }^2\theta$.
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   ${\sin }^2\theta -{\cos }^2\theta =-\frac{1}{2}$ (with $\theta =30^{\circ }$).

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7. Q47 Exemplar · Exercise 8.3
   Simplify $(1+{\tan }^2\theta )(1-\sin \theta )(1+\sin \theta )$.
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   $(1+{\tan }^2\theta )(1-\sin \theta )(1+\sin \theta )=1$.

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8. Q48 Exemplar · Exercise 8.3
   If $2{\sin }^2\theta -{\cos }^2\theta =2$, ​then ​find ​the ​value ​of $\theta$.
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   $\theta =90^{\circ }$.

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9. Q49 Exemplar · Exercise 8.3
   Show ​that $\frac{{\cos }^2(45^{\circ }+\theta )+{\cos }^2(45^{\circ }-\theta )}{\tan (60^{\circ }+\theta )\tan (30^{\circ }-\theta )}=1$.
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   The expression equals $1$ (proved).

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10. Q50 CBSE 2026
    If value ​of $\cot \theta$ ​is $\sqrt{5}$, ​then $\sin \theta$ ​equals

    1. (a)$\frac{1}{\sqrt{6}}$
    2. (b)$\sqrt{6}$
    3. (c)$\frac{\sqrt{5}}{6}$
    4. (d)$\frac{1}{2}$
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    (a) $\frac{1}{\sqrt{6}}$

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11. Q51 CBSE 2026
    If $x\cdot \tan 45^{\circ }\cdot \sin 30^{\circ }=\cos 30^{\circ }\cdot \cot 60^{\circ }$, ​then $x$ ​is equal ​to

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

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12. Q52 CBSE 2026
    Given that $\sin \theta =\frac{a}{b}$, ​then $\cos \theta$ is ​equal ​to :

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

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13. Q53 CBSE 2026
    If $\cos A=\frac{1}{2}$, then ​the value ​of ${\sin }^{2}A+2{\cos }^{2}A$ ​is ​:

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

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14. Q54 CBSE 2026
    If $\cos A=\frac{4}{5}$, ​then the ​value ​of $\tan A$ is ​:

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

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15. Q55 CBSE 2026
    If $2\sin A=1$, ​then ​the ​value ​of $\tan A+\cot A$ is ​:

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

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16. Q56 CBSE 2026
    When $\sin A=\frac{1}{3}$, ​the ​value ​of $\cot A$ is

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

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17. Q57 CBSE 2026
    If $\cos A=\frac{3}{5}$, ​then the ​value of $\tan A$ is:

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

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18. Q58 CBSE 2026
    $\frac{1+{\tan }^{2}A}{1+{\cot }^{2}A}$ ​equals ​to ​:

    1. (a)${\tan }^{2}A$
    2. (b)$-1$
    3. (c)$-{\tan }^{2}A$
    4. (d)${\cot }^{2}A$
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    (a) ${\tan }^{2}A$

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19. Q59 CBSE 2026
    The value ​of $(\cos 90^{\circ }-\sin 90^{\circ })$ is ​:

    1. (a)$-1$
    2. (b)greater than $0$
    3. (c)equal to the value of $\tan 45^{\circ }$
    4. (d)$0$
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    (a) $-1$

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20. Q60 CBSE 2026
    The ​value ​of $\frac{{\tan }^{2}60^{\circ }-1}{{\tan }^{2}60^{\circ }+1}$ ​is equal to ​the value ​of which of the following ?

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

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