Trigonometric Functions and Equation
EXERCISE - 4(B) PREVIOUS YEARS AIEEE/JEE (MAIN) ADVANCE LEVEL
SECTION - 1: SINGLE CHOICE CORRECT QUESTIONS
1. Letcos(a + f) = 2 and let sin(o. - B) = where 0
} iseqiil to: I 1
fa p
la |
a) pa 2) pa By, OG
6. If Sitan? x ~c0s?x) = 2eas2x'+9 , then the value of cos 4x is [JEE Main-2017]
7 2) 2 eS a
5 2-5 (8)-§ 3
7. Iisum of all the solutigfs ithe equation 8.05% (oo(E ' x) cos( 2 x) in (0, 4] is kx, then kis
é 6
equal to [JEE-MAIN-2018)]
8 0
5 @) Bs (>
i zt) ¢ 2 4
For any € | 4>> |; the expression sind — cost) + Glin + cost? + dsin“® equals:
[JEE-MAIN ONLINE-2019]
(1) 13 ~4 cos®e 7 (2) 18 ~ 4 costo + 2 sin"bcos“0
(3) 13 - 4 cos’ + 6 cos‘b (4) 13 - 4 cos’0 + 6 sin’bcos"0
The value of €08 Fp cos sings (JEE-MAIN ONLINE-2019]
1 9) 2 3) oe
id 5 ®) oe (9 Toa
a7, 10.
11.
12.
13.
14,
15.
16.
17.
18.
jathematics
The maximum velie of $cos)+Sxin( 0%) for any real value of: (SEE-MAIN ONLINE.2019]
v9 =
() Via 2) 2 4) 3a
10Sx-< 3, then the number of values of x for which sin x-sin2x-+sin3x = 0 i
[JEE-MAIN ONLINE-2019]
(2 (21 3 (a4
“The sum of all values of @ (a ) satisfying sin? 20 +.cos* 20 = 3 is: [JEE-MAIN ONLINE-2019]
"2
x 3x 5a
Ms ()x ay az
If sin’ +4cos'B+2=4V2sinacosB: a, B
11
M=——4Leos
(3) M= Ft gg
20. All possible values of 0 € [0, 2x] for which sin 20 + tan 20 > O lie in : [JEE MAINS - ONLINE - 2021]
o(0$)-(23) oles) (5e5) lo
aE) (ale
3
ela
Sa
21. HO
1
5 (2)
22. for xe(0. 5) Jodyosifix + 1oa,9c08x = =I and log;o[sftx +-Gosx) = 5 tlayon=1) n> 0, then the value
of nis equal to : [JEE MAINS - ONLINE - 2021]
(120 (2)12 (3)9 (4)16
23. ‘The number of roots of the equation, (81)"""* + (81)"°"* = 20 in the interval [0, =] is equal to:
[JEE MAINS - ONLINE - 2021]
3 (2)4 (3)8 (a2
24. The number of solutions of the equation x + 2 tanx = % in the interval [0, 2x] is :
2
[JEE MAINS - ONLINE - 2021)
a (2)4 (3)2 (as
25. The sum of all values of x in [0, 2x], for which sink + sin2x + sin3x + sindx = 0, isequal to:
[JEE MAINS - ONLINE - 2021]
(8x (2118 (3)12% (4)9%
54) ie:
[JEE MAINS - ONLINE - 2021]
1+sinx
=|tan2x|, x
The sum of solutions of the equation
w 35 @- jathematics
27. _Wn'sthe numberof solutions ofthe equation 2cosx{4sin| = +x in( 1]=1,x€10,m]andS isthe
sum of all these solutions, then the ordered pair (n, ) is (JEE MAINS - ONLINE - 2021]
138 2n 8n Sn
a (0%) @) (225) 8) (2) a) (3%)
‘SECTION -2: NUMERICAL ANSWER BASED QUESTIONS
eee (03),
, pee 5 and p= Fe ade n tan(a + 2p) is equal to
[JEE-MAIN ONLINE - 2020]
2. Let be the sum of all solutions (in radians) of the equation sin’ + cos*8-~sin0 cost) = Q in {0)4z). Then
is equal to [JEE MAINS - ONLINE - 2021]
ANSWER KEY
EXERCISE-4(B)
SECTION -1: SINGLE CHOICE CORRECT QUESTIONS
Que. 1 2 3 4 5 6 7 8 o 10
‘Ans. 2 3 4 3 3 2 2 1 3 1
ceca | NEA REL | || || J |
‘Ans. 1 1 2 1 1 1 3 4 1 4
Gre |S 2 Lap 8s eee
‘Ans. 2 2 2 1 4 1 1
SECTION -2: NUMERICAL ANSWER BASED QUESTIONS
Que. 1 2
‘Ans. 1 56