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Mathematics - Trigonometric Ratios & Identities

Practise 49 NTA Abhyas (JEE Main) questions on Trigonometric Ratios & Identities. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Trigonometric Ratios & Identities has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 49 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1In a triangle A B C , if sin A cos B = 1 4 and 3 tan A = tan B , then cot 2 A is equal to
  2. 2Let f x = m a x tan ⁡ x , cot ⁡ x . Then the number of roots of the equation f x = 1 2 in 0,2 π is
  3. 3If 1 + cos ⁡ 2 x sin ⁡ 2 x + 3 1 + tan ⁡ x tan ⁡ x 2 sin ⁡ x = 4 , then the value of tan ⁡ x can be equal to
  4. 4The value of the expression 1 + c o s e c π 4 + c o s e c π 8 + c o s e c π 16 is equal to
  5. 5The value of 1 + c o s π 8 1 + c o s 3 π 8 1 + c o s 5 π 8 1 + c o s 7 π 8 is equal to
  6. 6Let y = sin - 1 sin 8 - tan - 1 tan 1 0 + cos - 1 cos 1 2 - sec - 1 sec 9 + cot - 1 cot 6 - cosec - 1 cosec 7 . If y simplifies to a π + b t
  7. 7The value of sin ⁡ 9 π 14 sin ⁡ 11 π 14 sin ⁡ 13 π 14 is equal to
  8. 8If A , B , C are in arithmetic progression and B = π 4 , then tan ⁡ A tan ⁡ B tan ⁡ C =
  9. 9Let f = 1 1 + tan 2021 , then the value of = 1 89 f is equal to
  10. 10If 0 α π 16 and ( 1 + tan ⁡ α ) 1 + tan ⁡ 4 α = 2 , then the value of α is equal to
  11. 11If 0 3 , then sec is
  12. 12If a sin 2 ⁡ x + b cos 2 ⁡ x = c , b sin 2 ⁡ y + a cos 2 ⁡ y = d and a tan ⁡ x = b tan ⁡ y , then a 2 b 2 is equal to (Here a , b , c and d
  13. 13The difference between the greatest and the least possible value of the expression 3 - cos ⁡ x + sin 2 ⁡ x is
  14. 14The value of cos ⁡ π 11 cos ⁡ 2 π 11 cos ⁡ 3 π 11 … … cos ⁡ 11 π 11 is equal to
  15. 15The value of tan ⁡ 63 o - cot ⁡ 63 o is equal to
  16. 16The value of cot ⁡ 70 o + 4 cos ⁡ 70 o is
  17. 17If E = cos 2 ⁡ 71 o + cos 2 ⁡ 49 o + cos ⁡ 71 o cos ⁡ 49 o , then the value of 10 E is equal to
  18. 18If p = sin 2 ⁡ x + cos 4 ⁡ x , then
  19. 19The arithmetic mean of the numbers 2 sin ⁡ 2 o , 4 sin ⁡ 4 o , 6 sin ⁡ 6 o , … … . 178 sin ⁡ 178 o , 180 sin ⁡ 180 o is
  20. 20The maximum value of the expression sin ⁡ θ c o s 2 θ ∀ θ ∈ 0 , π is
  21. 21Let A = x 4 + 4 x 3 + 2 x 2 - 4 x + 7 where x = cot 11 8 and B = 1 - cos 8 tan 2 4 + 1 + cos 8 cot 2 4 where = 9 o , then the value of A B 2
  22. 22If 2 3 4 , then 2 tan + 1 c o s 2 is equal to
  23. 23If sin ⁡ θ = cos 2 ⁡ θ , then the value of cos 12 ⁡ θ + 3 cos 10 ⁡ θ + 3 cos 8 ⁡ θ + cos 6 ⁡ θ - 1 is equal to
  24. 24If the value of 1 + tan 1 o 1 + tan 2 o 1 + tan 3 o … … … . ( 1 + tan 44 o ) ( 1 + tan 45 o ) is 2 λ , then the sum of the digits of the num
  25. 25If 4 sin ⁡ 27 o = α - β , then the value of α + β is
  26. 26The expression sin ⁡ 27 ° cos ⁡ 57 ° sin ⁡ 87 ° simplifies to
  27. 27If s i n 23 π 24 = 2 p - q - 1 4 r , then the value of p 2 + q 2 - r 2 is equal to
  28. 28If 3 + cot 80 o cot 20 o cot 80 o + cot 20 o = t a n k , then the value of k is (where, k is an acute angle)
  29. 29Let f n = sin ⁡ 1 × sin ⁡ 2 × . . . . . s i n n , ∀ n ∈ N , then the number of elements in the set A = f 1 , f 2 , . . . . . . . . . . , f 6
  30. 30If F k = 1 + s i n 2 k 1 + sin k - 1 2 k 1 + sin 2 k + 1 2 k 1 + sin 3 k - 1 2 k , then the value of F 1 + F 2 + F 3 is equal to
  31. 31If x + y = 3 - cos ⁡ 4 θ and x - y = 4 sin ⁡ 2 θ , then the value of x + y is equal to
  32. 32If π θ 3 π 2 and cos ⁡ θ = - 3 5 , then t a n θ 4 is equal to
  33. 33If cos ⁡ 2 x + 2 cos ⁡ x = 1 , then sin 2 ⁡ x 2 - cos 2 ⁡ x is equal to
  34. 34Let the maximum and minimum value of the expression 2 cos 2 ⁡ θ + cos ⁡ θ + 1 is M and m respectively, then the value of M m is, (where [.]
  35. 35Three positive acute angles , and satisfy the relation tan 2 = 1 3 cot 2 and cot 2 = 1 2 3 tan 2 + cot 2 . Then, the value of + + is equal t
  36. 36The value of 2 sin 2 ⁡ θ + 4 cos ⁡ θ + α sin ⁡ α sin ⁡ θ + cos ⁡ 2 ( α + θ ) is
  37. 37t a n 6 2 0 o - 33 t a n 4 2 0 o + 27 t a n 2 2 0 o + 4 =
  38. 38If tan 25 o = a , then the value of tan ⁡ 205 o - tan ⁡ 115 o tan ⁡ 245 o + tan ⁡ 335 o in terms of a is
  39. 39If sin A and cos A are the roots of the equation 4 x 2 - 3 x + a = 0 , sin A + cos A + tan A + cot A + sec A + cosec A = 7 and 0 A 2 , then
  40. 40The angle between the minute hand and the hour hand of a clock at “half past 3 ” is equal to
  41. 41If 2 sin ⁡ α 1 + cos ⁡ α + sin ⁡ α = 3 4 , then the value of 1 - cos ⁡ α + sin ⁡ α 1 + sin ⁡ α is equal to
  42. 42If cos 5 = 5 c o s - 20 cos 3 + a cos 5 + b , then the value of a + b is equal to
  43. 43Let f x = sin ⁡ x + 3 sin ⁡ 3 x + 5 sin ⁡ 5 x + 3 sin ⁡ 7 x sin ⁡ 2 x + 2 sin ⁡ 4 x + 3 sin ⁡ 6 x , wherever defined. If x 1 + x 2 = π 2 , w
  44. 44If cos α + cos β = a , sin α + sin β = b and α - β = 2 θ , then cos 3 θ cos θ is equal to
  45. 45If sin ⁡ 2 β is the geometric mean between sin ⁡ α and cos ⁡ α , then cos ⁡ 4 β is equal to
  46. 46If sin 6 ⁡ θ + cos 6 ⁡ θ + k cos 2 ⁡ 2 θ = 1, then k is equal to
  47. 47If tan ⁡ θ = 3 tan ⁡ ϕ , then the maximum value of tan 2 ⁡ θ - ϕ is (where, tan ⁡ ϕ 0 )
  48. 48If 4 cos 36 o + c o t 7 1 2 = n 1 + n 2 + n 3 + n 4 + n 5 + n 6 , then the value of i = 1 6 n i 2 10 is equal to
  49. 49The value of the expression 2 ( s i n 1 ° + s i n 2 ° + s i n 3 ° + . . . . . . . . + s i n 89 ° ) 2 ( c o s 1 ° + c o s 2 ° + c o s 3 ° + .

Frequently Asked Questions

1.How many questions are available for Trigonometric Ratios & Identities?

This chapter includes 49 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

These are NTA Abhyas (JEE Main) questions specifically for the Trigonometric Ratios & Identities chapter. Questions from other exams like JEE Main or JEE Advanced are organised separately under their respective exam sections.

3.What is the difficulty level of Trigonometric Ratios & Identities questions in NTA Abhyas (JEE Main)?

Of the 49 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Trigonometric Ratios & Identities should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.