Introduction to Trigonometry class 10 Cbse presentation most expected questions and solution.

1. 1. Introduction to Trigonometry.
Quick revision and PYQs by Gangs Of Geniuses.

2. TRIGONOMETRIC RATIOS:

4. TRIGONOMETRIC VALUES: TRIGONOMETRIC IDENTITIES

7. 1. The value of ( tan2450-cos2600) is
(a)1/2
(b)1/4
(c) 3/2
(d)3/4

8. 2. Which of the following is not defined?
(a)Sec00
(b)Cosec 900
(c) Tan 900
(d)Cot 900

9. 3. In a right-angled triangle PQR, ∠𝑄=900. If ∠𝑃=450, then value of tan P – cos2 R is
(a)0
(b)1
(c) ½
(d)3/2

10. 4. If tan 𝜃 =
2
3
, then the value of sec𝜃 is
(a)
13
3
(b)
5
3
(c)
13
3
(d)
3
13

11. 5. If sin𝜃 -cos 𝜃 = 0, then the value of 𝜃 is
(a)300
(b)450
(c) 900
(d)00

12. 6.
1
1+𝑠𝑖𝑛 𝜃
+
1
1−𝑠𝑖𝑛 𝜃
can be simplified to get
a) 2 cos2 𝜃
b)
1
2
sec2 𝜃
𝑐)
1
2
sin2 𝜃
d) 2sec2 𝜃

13. 7. (1+tan2A) (1+sin A ) (1-sinA) is equal to
(a)
𝑐𝑜𝑠2𝐴
𝑠𝑒𝑐2 𝐴
(b)1
(c) 0
(d)2

14. 8. If cot 𝜃 =
1
3
the value of sec2 𝜃 + cosec2 𝜃 is
(a)1
(b)
40
9
(c)
38
9
(d)5
1
3

15. 9. In ∆𝐴𝐵𝐶 right angled at B, sin A=
7
25
, then the value of cosC is
(a)
7
25
(b)
24
25
(c)
7
24
(d)
24
7

16. 10. Given that sec 𝜃 = 2, the value of
1+𝑡𝑎𝑛𝜃
𝑠𝑖𝑛𝜃
is
(a)1
(b)
1
2
(c)
2
2
(d) 2

17. 11. If 𝜃 is an acute angle and tan 𝜃 + cot 𝜃 = 2, then the value of sin3 + cos3 𝜃 is
(a)1
(b)
1
2
(c)
2
2
(d) 2

18. 12. If a cot 𝜃+b cosec 𝜃 = p and b cot 𝜃 + a cosec 𝜃 = q, then p2-q2
(a)a2 – b2
(b)b2 – a2
(c) a2 + b2
(d)b – a

19. 13. if sec 𝜃 + tan 𝜃 p, then tan 𝜃 is
(a)
𝑝2+1
2𝑝
(b)
𝑝2−1
2𝑝
(c)
𝑝2−1
𝑝2+1
(d)
𝑝2+ 1
𝑝2−1

20. 14.
2
3
𝑠𝑖𝑛00 −
4
5
𝑐𝑜𝑠00 is equal to
(a)
2
3
(b)
−4
5
(c)0
(d)
−12
15

21. 15. Which of the following is true for all values of 𝜃(00 ≤
𝜃
≤
900) ?
(a)Cos2 𝜃-sin2 𝜃=1
(b)Cosec2 𝜃-sec2 𝜃=1
(c) Sec2 𝜃 – tan2 𝜃=1
(d)Cot2 𝜃 tan2 𝜃=1

22. 16. If tan A =
15
12
, find the value of (sin A + cos A) sec A.

23. 17. If tan A =
15
12
, find the value of (sin A + cos A) sec A.

24. 18. If 3x = cosec 𝜃 and
3
𝑥
= cot 𝜃, find the value of 3 𝑥2 −
1
𝑥2 .

25. 19. If tan(A+B)= 3 and tan(A-B) =
1
3
,A>B, then the value of A is _____.

26. 20. If 5tan 𝜃=3, then what is the value of
5 𝑠𝑖𝑛𝜃−3𝑐𝑜𝑠𝜃
4 𝑠𝑖𝑛𝜃 + 3 cos 𝜃
?

27. 21. The value of 𝑠𝑖𝑛2𝜃 +
1
1+𝑡𝑎𝑛2𝜃
= _________.

28. 22. The value of (1 + tan2 𝜃) (1-sin 𝜃) (1+sin 𝜃)= ____________.

29. 23. In a ∆𝐴𝐵𝐶, right-angled at C, if tanA =
1
3
, find the value of sinA CosB + cosA sinB.

31. 24. If cot 𝜃=
15
8
, then evaluate
(2+2𝑠𝑖𝑛𝜃)(1−𝑠𝑖𝑛𝜃)
(1+𝑐𝑜𝑠𝜃)(2−2𝑐𝑜𝑠𝜃)
.

33. 25. Prove that
1−𝑠𝑖𝑛𝜃
1+𝑠𝑖𝑛𝜃
. = sec 𝜃 - tan 𝜃

35. 26. Prove that
tan2 𝜃
1+tan2 𝜃
+
cot2 𝜃
1+cot2 𝜃
= 1

37. 27. The rod AC of a TV disc antenna is fixed at right angles to the wall, AB and a rod CD is
Supporting the disc as shown in Fig.4. if AC= 1.5m long and CD =3 m,
find (i) tan𝜃 (ii) sec𝜃 + cosec𝜃.

39. 28. If sin𝛼=
1
2
, then find the value of (3𝑐𝑜𝑠𝛼 − 4 cos2 𝛽).

41. 29. Evaluate: A)
5
𝑐𝑜𝑡2300 +
1
𝑠𝑖𝑛260o − 𝑐𝑜𝑡2450 + 2𝑠𝑖𝑛2900
(B) if θ is an acute angle and sin𝜃 = cos𝜃, find the value of tan2𝜃+ cot2 - 2.

43. 30. Prove that: (1+cot A + tan A)(sin A – cos A)= sin A tan A – cot A cos A.

45. 31. Prove the following:
(cosec A-Sin A)(Sec A-cos A) =
1
tan 𝐴+cot 𝐴

47. 32. If 4 tanθ = 3, evaluate
4 sin θ−cos θ+1
4 sin θ+cos θ−1

49. 33. Prove that: (sinθ + cosecθ)2 + (cosθ + secθ)2 = 7 + tan2θ + cot2θ

51. 34. Prove that: (1 + cotA – cosecA)(1+tan A + secA) = 2

53. 35. Prove that (1 + tan A – Sec A) x (1 + tan A + sec A) = 2 tan A

55. 36. Prove that
𝑐𝑜𝑠𝑒𝑐 θ
𝑐𝑜𝑠𝑒𝑐 θ−1
+
𝑐𝑜𝑠𝑒𝑐 θ
𝑐𝑜𝑠𝑒𝑐 θ+1
= 2 sec2θ

57. 37. If sinθ + cos θ = 3, then prove that tanθ + cotθ =1.

59. 38. Prove that
1+𝑡𝑎𝑛2𝐴
1+𝑐𝑜𝑡2𝐴 = sec2 A - 1

61. 39. Prove that
sin 𝐴−2𝑠𝑖𝑛3 𝐴
2𝑐𝑜𝑠3𝐴−cos 𝐴
= tan A

63. 40. Prove that sec A(1 - sinA)(secA + tanA) = 1

65. 41. Prove that
𝑠𝑖𝑛𝐴−2𝑠𝑖𝑛3𝐴
2𝑐𝑜𝑠3𝐴 −𝑐𝑜𝑠𝐴
= tanA

67. 42. Prove that
sin 𝐴−cos 𝐴+1
sin 𝐴+cos 𝐴−1
=
1
sec 𝐴−tan 𝐴

69. Thank You!
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