33
Chapter 8
Trigonometric Functions
ASSIGNMENT
Single Choice Type Questions
−4
1. If tan = , then sin is
3
−4 4 −4 4
(1) but not (2) or
5 5 5 5
4 5 4 5
(3) but not (4) and both
5 4 5 4
2. If A lies in the second quadrant and 3 tan A + 4 = 0, then the value of 2cotA – 5cosA + sinA is equal to
−53 23
(1) (2)
10 10
37 7
(3) (4)
10 10
3. The circular wire of diameter 10 cm is cut and placed along the circumference of a circle of diameter 1 m. The
angle subtended by the wire at the centre of the circle is equal to
(1) (2)
4 3
(3) (4)
5 10
4. The value of (secA + tanA – 1) (secA – tanA + 1) – 2tanA is equal to
(1) secA (2) 2secA
(3) 0 (4) 1
−1
5. If cos = and 0 360 , then the values of are
2
(1) 120°, 210° (2) 120°, 300°
(3) 60°, 240° (4) 120°, 240°
6. The value of sin15° + cos105° is
(1) 0 (2) 2sin15°
(3) cos15° + sin15° (4) sin15° – cos15°
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7. The value of cos1°.cos2°.....cos179° is
1
(1) (2) 0
2
(3) 1 (4) –1
8. If ABCD is a cyclic quadrilateral such that 12tanA – 5 = 0 and 5cosB+3 = 0, then the quadratic equation whose
roots are cosC and tanD is
(1) 39 x 2 − 16 x − 48 = 0 (2) 39 x 2 + 88 x + 48 = 0
(3) 39 x 2 − 88 x + 48 = 0 (4) 39 x 2 − 13 x − 46 = 0
2sin A 1+ sin A − cos A
9. If = k, then is
1+ sin A + cos A 1+ sin A
k
(1) (2) k
2
1
(3) 2k (4)
k
29
r 29
r S1
10. If cos 2 + = S1 and sin 2 + = S2, then S2
equals
r =15 r =15
(1) cot (2) tan
(3) –cot (4) –tan
11. The maximum value of cos2 (cos(33 + )) + sin2 ( sin(45 + )) is
(1) 1 + sin21 (2) 2
(3) 1 + cos21 (4) cos22
12. If a sin + b cos = m, b sin + a cos = n, a tan = b tan , then which of the following is true?
2 2 2
1 1 1 1 1 1 1 1
(1) − = − (2) + = +
n m a b n m a b
(3) m 2 + n 2 = a 2 + b 2 (4) m 2 − n 2 = a2 − b2
13. The value of cos12° + cos84° + cos156° + cos132° is
1
(1) (2) 1
2
−1 1
(3) (4)
2 8
14. In a ABC, if sinA – cosB = cosC, then the measure of B is
(1) (2)
2 3
(3) (4)
4 6
15. The value of cos ·cos ·cos ........cos n equals
4
8
16 2
1 1
(1) cosec n (2) n −1
cosec n −1
2n
2 2 2
1 1
(3) cosec n−1 (4) cosec n
2n 2 2n −1 2
n −1
r
16. cos2 n
is equal to
r =1
n n −1
(1) (2)
2 2
n n +1
(3) −1 (4)
2 2
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Trigonometric Functions JEE SCORE for Main-2025 35
3 5
17. cos + cos + cos = K cot , then K is equal to
14 14 14 14
1
(1) 1 (2)
2
(3) 2 (4) – 2
18. The value of 2tan18° + 3sec18° – 4cos18° is
(1) Zero (2) 5
(3) − 5 (4) 3
19. The expression 2sin2° + 4sin4° + 6sin6° + ........ 180sin180° equals
(1) cot1° (2) 90cot1°
(3) sin1° (4) 90cos1°
20. The value of tan (1 + sec)(1 + sec2) (1 + sec22) ........ (1 + sec2n) is
2
(1) tan2n (2) tan2n – 1
(3) tan2n + 1 (4) tan2n – 2
21. Let f(x) = cos10x + cos8x + 3cos4x + 3cos2x and g(x) = 8cosx·cos33x, then for all x we have
(1) f(x) = g(x) (2) 2f(x) = 3g(x)
(3) f(x) = 2g(x) (4) 2f(x) = g(x)
n
1
22. cos + cos(2r + 1) , n N is equal to
r =1
sin(n + 1) sin n
(1) (2)
sin ·cos n sin2 ·cos(n + 1)
tan(n + 1) sin(n − 1)
(3) (4)
sin n sin ·cos n
23. If x(0, 1), then greatest root of the equation sin2x = 2cos x is
1 1
(1) (2)
4 2
3 1
(3) (4)
4 3
24. If (0, 2) and 2sin2 – 5sin + 2 > 0, then the range of is
5
(1) 0, , 2 (2) 0, 6 ( , 2)
6 6
(3) 0, ( , 2) (4)
6
tan x tan2x
25. The general solution of the equation + + 2 = 0 is
tan2x tan x
n
(1) n (2)
3
(3) (2n −1) , n I (4) (3n 1) , n I
3 3
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36 JEE SCORE for Main-2025 Trigonometric Functions
n
26. STATEMENT-1 : The general solution of tan 5 = cot 2 is = + , n Z .
7 14
and
STATEMENT-2 : The equation cos = k has exactly two solutions in [0, 2] for all k, –1 k 1.
(1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(2) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
1 13
27. STATEMENT-1 : If cos = and cos = where and both are acute angles, then the value of – is .
7 14 3
and
1
STATEMENT-2 : cos = .
3 2
(1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(2) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
Numerical Value Type Questions
28. The number of solutions of equation 3cos2 + 5cos = 1 in [0, 2] is
6
29. The number of solutions of cos(rx ) = 6 in (0, 2] is
r =1
30. The number of solutions of the x + 2tan x = in [0, 2] is
2
31. The value of (cosecA.cosecB + cot A.cot B)2 − (cosecA.cot B + cosecB.cot A)2 is
32. If acos + bsin = 3 and asin – bcos = 4, then a2 + b2 has the value
1 1
33. If tan = and tan = , then the value of + is , then a equals
2 3 a
34. The value of sin(45° + ) – cos(45° – ) is
35. The value of sin50° – sin70° + sin10° is equal to
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ANSWERS
1. (2) 2. (2) 3. (3) 4. (3) 5. (4) 6. (1)
7. (2) 8. (1) 9. (2) 10. (1) 11. (1) 12. (2)
13. (3) 14. (1) 15. (4) 16. (3) 17. (2) 18. (1)
19. (2) 20. (1) 21. (1) 22. (2) 23. (3) 24. (1)
25. (4) 26. (3) 27. (4) 28. (2) 29. (1) 30. (3)
31. (1) 32. (25) 33. (4) 34. (0) 35. (0)
❑ ❑ ❑
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