Trigonometry (General & Higher Math)
Class: X
Time: 1 hour 30 min.
Total Marks: 60
Group A
Short Question
(23 × 1) + (2 × 2) + 3 = 30
1. If sin 𝜃 =
2
and cos 𝜃 = −
√7
1
√7
then cot 𝜃 is equal to:
2. The maximum value of (sin 𝜃 + cos 𝜃) is:
3. If sin 3𝜃 = 1 then 2𝜃 equals:
4. If 𝜃 is an acute angle and 4 sin 𝜃 = 3 then the value of 4 sin2 𝜃 − 3 cos 2 𝜃 + 2 is ___
1
5. If tan 𝜃 + tan 𝜃 = 2 then the value of 𝑐𝑜𝑠𝑒𝑐𝜃 is _____.
6. If cos 𝜃 =
1
2
, sin 𝛽 =
1
2
then the value of 𝜃 + 𝛽 is ____.
7. If 𝜃 increases from 0° to 90° then sin 𝜃 changes according to:
8. The word ‘Trigonometry’ is derived from _______ word. ‘Tri’ means three, ‘gon’
means edge and ‘métron’ means measure.
9. Trigonometry is the study of the relationship between the ______ and _______ of a
triangle.
10. There are evidences of using trigonometry in ________ and ________ civilization.
11. Alpha (𝛼), Beta (𝛽), Gamma (𝛾), Theta (𝜃), Phi (𝜑), Omega (𝜔) are _______ alphabet.
12. If ∠𝐵 = 90°, tan 𝐴 = 1 then find the value of 2 sin 𝐴 . cos 𝐴
13. cot 𝐴 is the multiplication of 𝑐𝑜𝑡 and 𝐴. Is the statement true or false?
14. 𝑐𝑜𝑠 is the short form of cosine. Is the statement true or false?
5
15. If sec(90° − 𝜃) = 3 find the value of 𝑐𝑜𝑠𝑒𝑐 𝜃 − cot 𝜃.
16. If cot(𝜃 − 30°) =
1
√3
, sin 𝜃 = ?
17. Trigonometry has two branches; one is plane trigonometry the other is __________.
18. −520° lies in which quadrant?
19. What is radian angle?
20. The centre angle produced by any arc of a circle is _______ to its arc.
21. 1 𝑟𝑎𝑑𝑖𝑎𝑛 = 57°17′ 81". Is this relation correct or wrong?
5
22. If tan 𝐴 = − 12 and tan 𝐴 , cos 𝐴 have opposite signs, find the value of sin 𝐴.
23. Convert 37°25′38" into radian.
24. Prove that: cos 𝑥 − cos 𝑥 . sin2 𝑥 = cos 3 𝑥
1−cos 𝜃
25. Prove that: (𝑐𝑜𝑠𝑒𝑐 𝜃 − cot 𝜃)2 = 1+cos 𝜃
26. Prove that:
sec 𝑥−cos 𝑥
1+cos 𝑥
= sec 𝑥 − 1
(2 marks)
(3 marks)
(2 marks)
Zaryan Abtahee
Group B
Creative Question
cot 𝐴+𝑐𝑜𝑠𝑒𝑐 𝐴−1
1. 𝑋 = cot 𝐴−𝑐𝑜𝑠𝑒𝑐 𝐴+1 and 𝑌 = cot 𝐴 − 𝑐𝑜𝑠𝑒𝑐 𝐴
a. If 𝐴 =
2𝜋
3
then find the value of Y
b. Prove that, 𝑋𝑌 = −1.
−1
c. If 𝑌 = (√3)
and 0 ≤ 𝐴 ≤ 2𝜋, then find the value of A.
𝑥
2. tan 𝜃 + sec 𝜃 = 𝑦 𝑎𝑛𝑑 𝜃 𝑖𝑠 𝑎𝑛 𝑎𝑐𝑢𝑡𝑒 𝑎𝑛𝑔𝑙𝑒.
a. 𝐼𝑓 𝜃 = 45° 𝑡ℎ𝑒𝑛 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡, 𝑥 =
𝑦
√2−1
b. 𝐼𝑓 𝑥 = 𝑦√3 𝑡ℎ𝑒𝑛 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝜃.
2𝑥𝑦
c. 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡, cos 𝜃 = 2 2
𝑥 +𝑦
3. cot 𝐴 + cos 𝐴 = 𝑝
𝑐𝑜𝑡𝐴 − cos 𝐴 = 𝑞
a. 𝑆ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 cot 2 𝐴 − cos 2 𝐴 = cot 2 𝐴 . cos 2 𝐴
16𝑝𝑞
b. 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡, (𝑝 − 𝑞 )2 = (𝑝+𝑞)2
4𝑝𝑞
c. 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡, 𝑐𝑜𝑠𝑒𝑐 𝐴 − sin 𝐴 = 𝑝2 −𝑞2
Zaryan Abtahee