DPP TRIGONOMETRY

TRIGONOMETRIC EQUATIONS AND IDENTITIES
**SINGLE OPTION CORRECT :-

1  1  tan 2 2A
Q.1 If A = 110° then equals
tan 2A
(A) tan A (B) – tan A (C) cot A (D) – cot A

Q.2 The maximum value of sin   cos  , is
3
(A) 1 (B) 2 (C) 24 (D) 2
Q.3 4 sin5° sin55° sin65° has the values equal to

(A)
31
(B)
31
(C)
31
(D)
d
3 3 1 i
2 2 2 2 2 2 2

1 1 1 1
Q.4 The sum    ......  is equal to
sin 45 sin 46 sin 47 sin 48 sin 49 sin 50 sin 133 sin 134
(A) sec (1)° (B) cosec (1)° (C) cot (1)° (D) none
Q.5 One side of a rectangular piece of paper is 6 cm, the adjacent sides being longer
than 6 cms. One corner of the paper is folded so that it sets on the opposite longer
side. If the length of the crease is l cms and it makes an angle  with the long side as
shown, then l is
3 6
(A) (B)
sin  cos2  2
sin cos 
3 3
(C) (D)
sin  cos  sin 3 

sin x sin 3x sin 9 x
Q.6 The value of the expression   equals
cos 3x cos 9 x cos 27 x
1 1 1 1
(A) (tan 9x – tan x) (B) (tan 9x – tan 3x) (C) (tan 27x – tan x) (D) (tan 27x – tan 3x)
2 2 2 2
2
 sec A cosec A 
Q.7 If A = 5° then the value of expression  2
 2
 is

 (1  4 sin A ) ( 4 cos A  1) 
(A) 6 (B) 8 (C) 16 (D) 24
Q.8 A circle is inscribed inside a regular pentagon and another circle is circumscribed about this pentagon.
Similarly a circle is inscribed in a regular heptagon and another circumscribed about the heptagon. The area
of the regions between the two circles in two cases are A1 and A2 respectively. If each polygon has a side
length of 2 units then which one of the following is true?
5 25 49
(A) A1 = A (B) A1 = A (C) A1 = A (D) A1 = A2
7 2 49 2 25 2




Prepared by Gaurav Sir