1
Pathshala JEE Crash Course
Trigonometry
1.


 3

 5

sin     .cos 
   .tan 
 
2
2
2






 7

.cot 
 
 2

is equal to:
(A) –sin2
(B) –cos2
(C) sin  . cos 
(D) –sin .cos 
24
and  lies in the second
25
quadrant, then sec  + tan  =
(A) –3
(B) –5
(C) –7
(D) –9
2.
If sin  
3.
If sin(  ) 
1
1
and cos(  )  where
2
2
 and  are positive acute angle, then
(A)  = 45°,  = 15°
(B)  = 15°,  = 45°
(C)  = 60°,  = 15°
(D)  = 20°,  = 40°
4.
If sin x1  sin x2  sin x3  .......  sin x2021 =
2021. Then value of cos x1  cos x2  .....
 cos x2021 
5.
Show that: (2cos x cos3 x  2cos5 x cos 7 x)
= cos 4 x  cos12 x .
6.
7.
Show that:
 3

 3

cos   x   cos   x    2 sin x .
4
4




Prove that:


tan   x 
2
4

   1  tan x 


1  tan x 


tan   x  
4

8.
DPP-01
If sin 2 + sin2 
then cos2 ( – ) =
3
(A)
8
3
(C)
4
9.
1
3
, cos 2 + cos2 
2
2
5
8
5
(D)
4
(B)
The maximum value of


5cos   3cos      3 is
3

(A) 5
(B) 10
(C) 11
(D) –1
10.
3cos   cos3
is equal to:
3sin   sin 3
(A) 1 + cot2
(B) cot4
(C) cot3
(D) 2 cot
1
1
 2cos  , then x 3  3 
x
x
(A) cos3
(B) 2 cos3
1
1
(C) cos3
(D)
cos3
2
3
11. If x 
12. sin224° – sin26° is equal to
(A)
5 1
4
(B)
5 1
8
(C)
5 1
4
(D)
5 1
8

, then the value of
4
(cotA – 1)(cotB – 1) =
(A) 1
(B) 2
(C) 3
(D) 4
13. If A  B 
2
14. The value of is
    2   3   5 
2sin   sin   sin   sin  
8  8   8   8 
 6   7  
sin   sin  
 8   8 
[JEE Main - 2021]
1
1
(A)
(B)
4
4 2
1
1
(C)
(D)
8
8 2
15. If 15sin4 + 10cos4 = 6, for some   R,
then the value of 27sec6 + 8cosec6 is
equal to
[JEE Main-2021]
(A) 500
(B) 400
(C) 250
(D) 350
16. The value of

 3 
    3 
cos3   cos    sin 3   sin   is :
8
 8 
8  8 
[JEE Main-2020]
1
1
(A)
(B)
2
2
1
1
(C)
(D)
4
2 2
17. If cos( + ) = 3/5 , sin( – ) = 5/13 and 0

< ,  < , then tan(2) is equal to:
4
[JEE Main-2019]
(A) 21/16
(B) 63/52
(C) 33/52
(D) 63/16
18. The value of sin10° sin30° sin50° sin70° is
[JEE Main-2019]
1
1
(A)
(B)
36
16
1
1
(C)
(D)
18
32
19. If the equation cos4 + sin4 +  = 0 has real
solutions for , then  lies in the interval
[JEE Main-2020]
 3 5
 1 1
(A)   ,  
(B)   ,  
 2 4
 2 4
1
 5


(C)   , 1
(D)  1,  
2
 4


20. The number of integral values of ‘k’ for
which the equation 3sinx + 4cosx = k + 1 has
a solution, k  R is ____. [JEE Main-2021]
3
ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
(C)
(C)
(A)
(0)
(Proof)
(Proof)
(Proof)
(B)
(B)
(C)
(B)
12.
13.
14.
15.
16.
17.
18.
19.
20.
(B)
(B)
(C)
(C)
(D)
(D)
(B)
(D)
11
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