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Class X Trigonometric Identities DPP

The document provides a series of trigonometric identities and proofs aimed at Class X mathematics students. It includes various identities involving sine, cosine, secant, and cosecant functions, along with problems for students to prove. The content is structured with references to CBSE examinations, indicating its educational purpose.

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56 views1 page

Class X Trigonometric Identities DPP

The document provides a series of trigonometric identities and proofs aimed at Class X mathematics students. It includes various identities involving sine, cosine, secant, and cosecant functions, along with problems for students to prove. The content is structured with references to CBSE examinations, indicating its educational purpose.

Uploaded by

thetactician619
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Trigonometric Identities (Class X) Mathematics

DPP
1 1
1.   2 sec 2 A
1  sin A 1  sin A

sin  1  cos 
2.   2cosec (CBSE 2000)
  cos  sin 

1  cos A sin A
3. 
sin A 1  cos A

4. cos ec2   sec 2   cos ec 2 sec2  [CBSE 2001)

5. Prove the following identities : (CBSE 2000)

(i) (sin  + cosec  )2 + (cos  + sec  )2 = 7 + tan2  + cot2 

(ii) (sin  + sec  )2 + (cos  + cosec  )2 = (1 + sec  cosec  )2 (CBSE 2000)

sin   cos  sin   cos  2 2 2


(iii)     (CBSE 2000)
sin   cos  sin   cos  sin2   cos 2  2sin2   1 1  2 cos 2 

(iv) (cosec  – sin  ) (sec  – cos  ) (tan  + cot  ) = 1

(v) tan2  + cot2  + 2 = sec2  cosec2 

6. Prove the following identities :

sin2  cos 2  1
(i)   2
cos  sin  sin  cos 2 
2 2 2

(1  sin )2  (1  sin )2  1  sin2  


(ii)  2  
cos 2  2
   sin  

(1  cot   tan )(sin   cos )


(iii)  sin2  cos 2 
sec 3   cosec 3 

7. cosec6  = cot6  + 3cot2  cosec2  +1

 1  1
8. (1  tan2 A)  1   (CBSE 2006)
 tan A  sin A  sin4 A
2 2

2 2
 1      1  sin2  
9.  tan    tan    2
 cos    cos      sin2  
 

10. Prove the following identities :

sin   2sin3 
(i)  tan  (CBSE 2018)
2 cos 3   cos 

1 1 1 1
(ii)    (CBSE 2002)
cosec   cot  sin  sin  cosec   cot 

(iii) 2(sin6   cos 6 )  3(sin4   cos 4 )  1  0


(iv) (sin8   cos 8 )  (sin2   cos 2 )(1  2sin2  cos 2 )

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