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 19 of 23

1. Q361 CBSE 2020
   If $\tan \theta =\frac{2}{3}$, ​then ​the ​value of ${\cos }^2\theta -{\sin }^2\theta$ is ​____ .
   Show answer

   ${\cos }^2\theta -{\sin }^2\theta =\frac{5}{13}$

   Step-by-step solution →
2. Q362 CBSE 2020
   If $\sin \theta =\frac{5}{13}$, then the ​value ​of $\tan \theta$ ​is ​________.
   Show answer

   $\tan \theta =\frac{5}{12}$

   Step-by-step solution →
3. Q363 CBSE 2020
   The ​value ​of $({\cos }^{2}45^{\circ }+{\cot }^{2}45^{\circ })$ ​is ________.
   Show answer

   ${\cos }^{2}45^{\circ }+{\cot }^{2}45^{\circ }=\frac{3}{2}$.

   Step-by-step solution →
4. Q364 CBSE 2020
   The value of $(\sin 20^{\circ }\cos 70^{\circ }+\sin 70^{\circ }\cos 20^{\circ })$ ​is ​__________.
   Show answer

   $1$

   Step-by-step solution →
5. Q365 CBSE 2020
   If $\tan (A+B)=\sqrt{3}$ ​and $\tan (A-B)=\frac{1}{\sqrt{3}}$, $A>B$, ​then the value of $A$ ​is ​____.
   Show answer

   $A=45^{\circ }$.

   Step-by-step solution →
6. Q366 CBSE 2020
   $\frac{\cos 80^{\circ }}{\sin 10^{\circ }}+\cos 59^{\circ }\csc 31^{\circ }=$ ​______.
   Show answer

   $\frac{\cos 80^{\circ }}{\sin 10^{\circ }}+\cos 59^{\circ }\csc 31^{\circ }=2$

   Step-by-step solution →
7. Q367 CBSE 2020
   The ​value of $(\tan 27^{\circ }-\cot 63^{\circ })$ ​is ​________.
   Show answer

   $\tan 27^{\circ }-\cot 63^{\circ }=0$.

   Step-by-step solution →
8. Q368 CBSE 2020
   If $\tan A=1$, then $2\sin A\cos A=$ ​________ ​.
   Show answer

   $2\sin A\cos A=1$

   Step-by-step solution →
9. Q369 CBSE 2020
   The value ​of $({\tan }^{2}60^{\circ }+{\sin }^{2}45^{\circ })$ ​is ​________.
   Show answer

   ${\tan }^{2}60^{\circ }+{\sin }^{2}45^{\circ }=\frac{7}{2}=3.5$

   Step-by-step solution →
10. Q370 CBSE 2020
    $\frac{3\cot 40^{\circ }}{\tan 50^{\circ }}-\frac{1}{2}\left(\frac{\cos 35^{\circ }}{\sin 55^{\circ }}\right)=$ ​__________.
    Show answer

    The value is $\frac{5}{2}$ (i.e. $2.5$).

    Step-by-step solution →
11. Q371 CBSE 2020
    The ​value ​of $(\tan 1^{\circ }\tan 2^{\circ }\dots \dots \tan 89^{\circ })$ ​is ​equal to __________.
    Show answer

    The value is $1$.

    Step-by-step solution →
12. Q372 CBSE 2020
    If $\cot \theta =\frac{7}{8}$, ​then the ​value ​of $\frac{(1+\sin \theta )(1-\sin \theta )}{(1+\cos \theta )(1-\cos \theta )}=$ ________.
    Show answer

    $\frac{49}{64}$

    Step-by-step solution →
13. Q373 CBSE 2020
    The ​value ​of $\left({\sin }^2\theta +\frac{1}{1+{\tan }^2\theta }\right)=$ ________ ​.
    Show answer

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

    Step-by-step solution →
14. Q374 CBSE 2020
    The ​value ​of $(1+{\tan }^2\theta )(1-\sin \theta )(1+\sin \theta )=$ ​______.
    Show answer

    $(1+{\tan }^2\theta )(1-\sin \theta )(1+\sin \theta )=1$.

    Step-by-step solution →
15. Q375 CBSE 2020
    If $5\tan \theta =3$, ​then ​what is ​the ​value ​of $\left(\frac{5\sin \theta -3\cos \theta }{4\sin \theta +3\cos \theta }\right)$?
    Show answer

    The value of the expression is $0$.

    Step-by-step solution →
16. Q376 CBSE 2020
    What is ​the ​value of $\left(\frac{1}{1+{\cot }^2\theta }+\frac{1}{1+{\tan }^2\theta }\right)$ ​?
    Show answer

    The value is $1$.

    Step-by-step solution →
17. Q377 CBSE 2020
    If $\sin A+{\sin }^{2}A=1$, then ​find the value of ​the ​expression $({\cos }^{2}A+{\cos }^{4}A)$.
    Show answer

    ${\cos }^{2}A+{\cos }^{4}A=1$.

    Step-by-step solution →
18. Q378 CBSE 2020
    Find the ​value ​of $(\cos 48^{\circ }-\sin 42^{\circ })$.
    Show answer

    $\cos 48^{\circ }-\sin 42^{\circ }=0$

    Step-by-step solution →
19. Q379 CBSE 2020
    If $\sec \theta =\frac{25}{7}$, ​then ​find ​the ​value ​of $\cot \theta$.
    Show answer

    $\cot \theta =\frac{7}{24}$

    Step-by-step solution →
20. Q380 CBSE 2020
    If $3\tan \theta =4$, then ​find ​the ​value ​of $\left(\frac{3\sin \theta +2\cos \theta }{3\sin \theta -2\cos \theta }\right)$.
    Show answer

    $\frac{3\sin \theta +2\cos \theta }{3\sin \theta -2\cos \theta }=3$

    Step-by-step solution →