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UDAAN 2026
Maths Practice Sheet
Trigonometry

1. Prove that: (i) If D is the mid point of AC, then find BD.
1 − cos A 1 + cos A (ii) Find the measures of A and C.
+ = cosec A (iii) Find the value of sin A + cos C.
1 + cos A 1 − cos A
10. If m = cos A – sin A and n = cos A + sin A, then show
1 − sin A
Prove that: ( sec A − tan A) =
2
2. m n 4sin A cos A 4
1 + sin A that − = =−
2
n m cos A − sin A 2 cot A − tan A
1 1
3. Prove that: + = 2cosec A cot A 11. If sin  – cos  = 0, then find the value of
sec A − 1 sec A + 1
(sin4  + cos4 ).
tan A + tan B
4. Prove that: = tan A tan B cosec A − cot A cosec A + cot A
cot A + cot B 12. Prove that : + =
cosec A + cot A cosec A − cot A
5. Prove that:  1 + cos2 A 
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B ( )
2 cosec2 A − 1 = 2 
 1 − cos2 A 
 

6. If sin  + cos  = 3 , then find the value of sin  cos  . 13. Prove that :

7. Prove that: sec3  cosec3 
1 + = sec  cosec  ( sec  + cosec )
( cosec A − sin A)(sec A − cos A) = sec2  − 1 cosec2  − 1
cot A + tan A

cos2 
8. Show that: sin6 A + 3sin2 A cos2 A = 1 − cos6 A 14. If  is acute and = 3 , then  is equal to:
cot 2  − cos2 
9. Aanya and her father go to meet her friend Juhi for a (A) 60° (B) 30°
(C) 90° (D) None of these
party. When they reached to Juhi's place, Aanya saw
the roof of the house, which is triangular in shape. If
she imagined the dimensions of the roof as given in the 11cos  − 7sin 
15. If 4 cos  = 11 sin , then the value of
figure, then answer the following questions. 11cos  + 7sin 
is:
(A) 93/149 (B) 94/149
(C) 91/149 (D) 97/149

16. tan2  sin2  is equal to:
(A) tan2  – sin2  (B) tan2  + sin2 
tan 2 
(C) (D) sin2  cot2 
sin 2 

17. If 3sec (3x − 21)  = 2 , then find the value of
sin2 ( x + 13)  + cot 2 ( x + 13)  .

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