INTRODUCTION TO TRIGONOMETRY

Black holes result from God dividing the universe by zero.

By O.P. GUPTA Math Mentor

INDIRA AWARD WINNER

 For detailed solutions, check YouTube Channel.

YouTube.com/MathematiciaByOPGupta

 Multiple Choice Questions, with only one correct option.

Q01. If x  r sin θ and y  r cosθ then, the value of x 2  y 2 is:
1
(a) r (b) r 2 (c) (d) 1
r
Q02. The value of cosec70o  sec 20o is:
(a) 0 (b) 1 (c) 90o (d) 50o
Q03. If 3secθ  5  0 then, cot  is equal to:
5 4 3 3
(a) (b) (c) (d)
3 5 4 5
Q04. If θ  45o then, sec θ cot θ  cosecθ tan θ is:
(a) 0 (b) 1 (c) 2 2 (d) 2
Q05. If sin(90o  θ) cos θ  1 and θ is an acute angle then, θ is:
(a) 90o (b) 60o (c) 30o (d) None of these
Q06. Triangle TRY is a right angled isosceles triangle then, cos T  cos R  cos Y is:
1
(a) 2 (b) 2 2 (c) 1  2 2 (d) 1 
2
AC 3
Q07. If triangles ABC and PRT are similar such that C  R  90o and  then, sin T is:
AB 5
3 5 4 5
(a) (b) (c) (d)
5 3 5 4
Q08. If k  7sec2 62o  7 cot 2 28o  7sec 0o then, the value of k is:
1
(a) 1 (b) 0 (c) 7 (d)
7
Q09. The value of cot θ  sin  90o  θ  cos  90o  θ  is:

MATHEMATICIA By O.P. GUPTA : MCQ in Mathematics (Class 10) 1

MATHEMATICIA for Class 10 By O.P. GUPTA (INDIRA Award Winner)

(a) cot θ (b) cos2 θ (c) cot 2 θ (d) cot θ cos2 θ

sin θ
Q10. can also be written as:
1  sin 2 θ
sin θ
(a) cot θ (b) sin θ (c) (d) tan θ
cos θ

sin 2 20o  sin 2 70o sec 60o

Q11. If  then, the value of k is:
2  cos2 69o  cos2 21o  k

(a) 1 (b) 2 (c) 3 (d) 4

Q12. 1  tan 2  equals:
(a) sec  (b) sec 2  (c) sec 2 (d) cot 2 
13
Q13. If cosec   , then
12
12 5 12 12
(a) tan   (b) tan    (c) tan   (d) tan   
5 12 25 25
Q14. cot   tan  equals:
(a) cosec  sec  (b) sin  sec  (c) cos  tan  (d) sin 2 
Q15. cos1o.cos 2o.cos3o.....cos180o  _____?
(a) 1 (b) –1 (c) 0 (d) None of these
1 1
Q16. If sin  A  B  and cos  A  B   then, A and B will be, respectively:
2 2
(a) 15º, 45º (b) 45º, 15º (c) 45º, 45º (d) 30º, 60º
Q17. If sin   sin 2   1 , then the value of cos2   cos 4  will be:
(a) 1 (b) 2sin 2  (c) 1  2sin 2  (d) Can’t be determined
Q18. If sin A  cos A  2 cos(90o  A) , then cot A is equal to:

(a) 1  2 (b) 2 1 (c) 2 1 (d) 2  2

Q19. If sin  A  B  0.5 , cos  A  B   0.5 ; 0o  A  B  90o , A  B then, values of A and
B are:
(a) A  45o , B  15o (b) A  55o , B  25o

(c) A  35o , B  25o (d) None of these

Q20. An isosceles triangle ABC in which AB  AC and B  70o then angle A is:
(a) 30 (b) 40 (c) 70 (d) 140
Q21. If sin 3A  cos(A  26o ) , where 3A is an acute angle, then the value of A is:
(a) 29º (b) 15º (c) 30º (d) None of these

2 MATHEMATICIA By O.P. GUPTA : MCQ in Mathematics (Class 10)

For all the Math-Gyan, visit at THEOPGUPTA.COM  WhatsApp @ +919650350480

Q22.
1  tan A   __________?
2

1  cot A  2

(a) sec2 A (b) –1 (c) cot 2 A (d) tan 2 A

cos 60o  sin 60o
Q23.  ................... :
cos 60o  sin 60o
(a)  3  2 (b) 2  3 (c) 32 (d) None of these
Q24. The value of tan 5º tan 10º tan 15º tan 20º tan 70º tan 75º tan 80º tan 85º is:
(a) 0 (b) 1 (c) 2 (d) None of these
12 13sin A  5sec A
Q25. If sin A  , then the value of will be:
13 5tan A  12cosec A
(a) 9 (b) 8 (c) 4 (d) None of these
Q26. The value of tan 30º sin 30º cot 60º cosec 30º will be:
1 1
(a) 1 (b) (c) (d) 3
3 3
Q27. If  = 45º, then the value of cos2   sin 2  will be:
1 1
(a) 0 (b)  (c) (d) None of these
2 2
Q28. If sin   cos  , then the value of  will be:
(a) 60º (b) 30º (c) 45º (d) None of these
Q29. If  is an acute angle and 7  4 sin   9 , then the value of  is:
(a) 90º (b) 30º (c) 45º (d) 60º
Q30. If  increases from 0o to 90o then, sin  changes according to:
(a) from –∞ to 0 (b) from 0 to 1 (c) from –∞ to 1 (d) None of these
Q31. If sin 2A  cos 3A , then correct statement is:
(a) A  110o (b) A  30o (c) A  20o (d) A  18o
Q32. If     90o and   2 , then cos2   sin 2  is equal to:
1
(a) 1 (b) (c) 0 (d) 2
2
Q33. If A  B  45o , the value of (cos A cos B  sin A sin B) is:

3 1
(a) (b) 0 (c) (d) None of these
2 2
Q34. The value of , for sin 2θ  1, 0o  θ  90o is:
(a) 60o (b) 55o (c) 45o (d) 135o

MATHEMATICIA By O.P. GUPTA : MCQ in Mathematics (Class 10) 3

MATHEMATICIA for Class 10 By O.P. GUPTA (INDIRA Award Winner)

Q35. Value of sec 2 26o  cot 2 64 o is:

(a) 0 (b) 1 (c) –1 (d) 2
Q36. The value of tan1o tan 2o tan 3o..... tan 89o is:
(a) 0 (b) 1 (c) –1 (d) 90

Q37. 1  tan 2 θ is equal to:

(a) cot θ (b) cosθ (c) cosecθ (d) secθ
3
Q38. If α  β  90o , cot β  then, tan α is equal to:
4
3 4 1 1
(a) (b) (c) (d)
4 3 4 3
1
Q39. Maximum value of , 0o  θ  90o is:
cosecθ
(a) –1 (b) 2 (c) 1 (d) Can’t be determined
1 1
Q40. If cos θ  , sin β  then value of θ  β :
2 2
(a) 30o (b) 60o (c) 90o (d) 120o
Q41. If sin  A  B  1  cos  A  B then:

(a) A  B  90o (b) A  B  0o (c) A  B  45o (d) A  2B

Q42. The maximum value of (sin   cos ) is:

(a) 1 (b) 2 (c) 2 (d) 2 2

Q43. If sec 4A  cosec(A  20o ) , the value of A is:
(a) 25º (b) 15º (c) 22º (d) 35º
Q44. 9sec2 A  9 tan 2 A  ______?
(a) 1 (b) 9 (c) 8 (d) 0
1  tan 2 45o
Q45.  ___?
1  tan 2 45o
(a) tan 90o (b) 1 (c) sin 45o (d) 0
Q46. cos 0o  ____?
(a) 0 (b) 1 (c) not defined (d) None of these
Q47. tan x  sin x  m and tan x  sin x  n , then (m 2  n 2 ) is equal to:

(a) 4 mn (b) mn (c) 2 mn (d) None of these

Q48. If x  r sin A cos C and y  r sin A sin C and z  r cos A , then the value of x 2  y 2  z 2 is:

4 MATHEMATICIA By O.P. GUPTA : MCQ in Mathematics (Class 10)

For all the Math-Gyan, visit at THEOPGUPTA.COM  WhatsApp @ +919650350480

1 r2 r
(a) (b) r 2 (c) (d)
r2 2 2
Q49. If sin 3  1 then, 2 equals:
(a) 30o (b) 60o (c) 45o (d) 90o
Q50. In a right angled triangle, one of the side lengths is 24 units, while the other one is 7 units. Also
the angle between longest and shortest sides is known to be  . Assuming that the shortest side of
triangle represents its base, value of sin  is:
7 24 24
(a) (b) (c) (d) Data insufficient
24 7 25

MATHEMATICIA By O.P. GUPTA : MCQ in Mathematics (Class 10) 5

MATHEMATICIA for Class 10 By O.P. GUPTA (INDIRA Award Winner)

ANSWERS KEY
Q01. b Q02. a Q03. c Q04. a Q05. d Q06. a Q07. a
Q08. b Q09. d Q10. d Q11. d Q12. b Q13. a Q14. a
Q15. c Q16. b Q17. a Q18. c Q19. a Q20. b Q21. a
Q22. d Q23. b Q24. b Q25. d Q26. b Q27. a Q28. c
Q29. b Q30. b Q31. d Q32. b Q33. c Q34. c Q35. b
Q36. b Q37. d Q38. a Q39. c Q40. c Q41. c Q42. b
Q43. c Q44. b Q45. d Q46. b Q47. a Q48. b Q49. b
Q50. c

# Dear math scholars,

We have taken utmost care while preparing this draft. Still chances of human error can’t be ruled out.
Please inform us about any Typing error / mistake in this document.
This will help many future learners of Mathematics.

Email ID - iMathematicia@gmail.com
WhatsApp @ +91 9650350480 (only message)

O.P. GUPTA, Math Mentor

[Maths (Hons.), E & C Engg., Indira Award Winner]
Follow us on Twitter @theopgupta
Follow us on Instagram @theopgupta
Official Website : www.theOPGupta.com

YouTube.com/MathematiciaByOPGupta

 Buy our Books, Test Papers and Sample Papers at theopgupta.com

6 MATHEMATICIA By O.P. GUPTA : MCQ in Mathematics (Class 10)