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Mathematics - Trigonometric Equations

Practise 83 NTA Abhyas (JEE Main) questions on Trigonometric Equations. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Trigonometric Equations has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 83 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. 1If the expression ( 1 + tan x + tan 2 x ) ( 1 - cot x + cot 2 x ) is positive, then the complete set of values of x is
  2. 2If 3 sin ⁡ x + cos ⁡ x - 2 = y - 1 2 for 0 ≤ x ≤ 8 π, then the number of values of the pair x , y is equal to
  3. 3The total number of solutions of the equation sin x tan 4 x = cos x for all x 0 , are
  4. 4The number of solutions to the equation 2 e sin ⁡ x - 3 - e 2 sin ⁡ x = e sin ⁡ x - e 2 sin ⁡ x - 1 in 0,2 π is
  5. 5The set {x R : cos 2 x + 2 cos 2 x = 2 } is equal to
  6. 6If and are the solutions of s i n x = - 1 2 in 0,2 and and are the solutions of cos x = - 3 2 in 0,2 , then the value of + - is equal to
  7. 7If x and y are the solutions of the equation 5 + 8 s i n 2 x = 2 y 2 - 8 y + 21 , then the least possible value of x 2 y 3 is
  8. 8The number of solutions of the equation cot 2 ⁡ sin ⁡ x + 3 = 1 in 0,3 π is equal to
  9. 9The number of solutions of the equation l o g 2 sin x ( 1 + cos x ) = 2 in the interval 0 , 5 is
  10. 10The number of solutions of the equation tan ⁡ x + sec ⁡ x = 2 cos ⁡ x lying in the interval 0,5 π is
  11. 11The sum of roots of the equation s i n 4 x - c o s 2 x s i n x + 2 s i n 2 x + s i n x = 0 for 0 x 3 is equal to
  12. 12Let 0 θ 1 θ 2 θ 3 … denotes the positive solutions of the equation 3 + 3 cos ⁡ θ = 2 sin 2 ⁡ θ . If θ 3 + θ 7 = a π , where a is an integer,
  13. 13If 1 6 sin θ , cos θ and tan ⁡ θ are in geometric progression, then the complete solution set of θ is
  14. 14The number of ordered pairs a , x satisfying the equation sec 2 a + 2 x + a 2 - 1 = 0 , - x is
  15. 15The number of solutions in the interval 0 , π of the equation sin 3 ⁡ x cos ⁡ 3 x + sin ⁡ 3 x cos 3 ⁡ x = 0 is equal to
  16. 16The number of values of x lying in the interval - 2 π , 2 π satisfying the equation 1 + cos ⁡ 10 x cos ⁡ 6 x = 2 c o s 2 8 x + s i n 2 8 x i
  17. 17c o s e c 2 θ cos 2 θ - 3 cos ⁡ θ + 2 ≥ 1 , if θ belongs to
  18. 18If the equation x 2 + 4 + 3 sin ⁡ a x + b - 2 x = 0 has atleast one real solution, where a , b ∈ [ 0, 2 π ] , then one possible value of ( a
  19. 19The solution of the equation tan 2 ⁡ x - 1 - 1 = 1 + cos ⁡ 2 x is
  20. 20The number of values of x in the interval 0 , 5 π satisfying the equation 3 sin 2 ⁡ x - 7 sin ⁡ x + 2 = 0 is
  21. 21The number of values of θ ∈ − 3 π 2 , 4 π 3 which satisfies the system of equations 2 sin 2 θ + sin 2 2 θ = 2 and sin 2 θ + cos 2 θ = tan θ
  22. 22The number of values of x ∈ - 2 π , 2 π which satisfy the equation c o s e c x = 1 + cot ⁡ x is equal to
  23. 23In the interval - π 2 , π 2 , the equation log sin ⁡ θ ⁡ cos ⁡ 2 θ = 2 has
  24. 24If sin ⁡ x + cos ⁡ y = 1 3 and cos ⁡ x + sin ⁡ y = 3 4 , then the value of tan ⁡ x - y 2 is equal to
  25. 25If tan ⁡ k + 1 θ = tan ⁡ θ , then the set of all the values of θ is
  26. 26The solution of the equation sin 2 ⁡ x + cos 2 ⁡ 3 x = 1 is
  27. 27The equation t a n 4 x - 2 s e c 2 x + a 2 = 0 will have at least one solution, if
  28. 28The sum of all the solutions in 0,100 for the equation sin ⁡ π x + cos ⁡ π x = 0 is
  29. 29If sin 3 ⁡ θ - cos 3 ⁡ θ sin ⁡ θ - cos ⁡ θ - cos ⁡ θ 1 + cot 2 ⁡ θ - 2 tan ⁡ θ cot ⁡ θ = - 1 ∀ θ ∈ 0 , 2 π , then
  30. 30The number of solutions of the equation sin 3 ⁡ x cos ⁡ x + sin 2 ⁡ x cos 2 ⁡ x + cos 3 ⁡ x sin ⁡ x + 1 = 0 in the interval 0 , 2 π is equal
  31. 31For - 2 x 2 , the number of points of intersection of curves y = cos x and y = sin 3 x is
  32. 32If tan 2 x + y + cot 2 x + y = 1 - 2 x - x 2 , then w h e r e , n Z
  33. 33The number of ordered pairs ( x , y ) satisfying the equations y = 2 sin ⁡ x a n d y = 5 x 2 + 2 x + 3 is/are
  34. 34General solution of the equation 4 cot ⁡ 2 θ + t a n 2 θ = cot 2 ⁡ θ is (where, n ∈ Z )
  35. 35The number of solutions of the equation sin x ⋅ sin 2 x ⋅ sin 3 x ⋅ sin 4 x ⋅ sin 5 x = 0 in 0 , π is equal to
  36. 36Number of solutions of 2 s i n ( | x | ) = 3 | c o s x | in [ − π , π ] , is equal to
  37. 37If 0 A B , sin A - sin B = 1 2 and cos A - cos B = 3 2 , then the value of A + B is equal to
  38. 38The number of solutions of the equation tan x sin x - 1 = tan x - sin x , x 0,2 is equal to.
  39. 39If 0 , and cos + cos - c o s + = 3 2 , then the value of 3 sin + cos is equal to
  40. 40The number of solutions of the equation 3 + cos ⁡ x 2 = 4 - 2 sin 8 ⁡ x in 0 , 9 π is equal to
  41. 41The number of solutions, the equation s i n 4 x + c o s 4 x = s i n x c o s x has, in [ π , 5 π ] is/are
  42. 42The number of values of the parameter α ∈ 0 , 2 π for which the quadratic function sin ⁡ α x 2 + 2 cos ⁡ α x + 1 2 cos ⁡ α + sin ⁡ α is the
  43. 43If c o s x - s i n x = - 5 4 , where π 2 x 3 π 4 , then c o t x 2 is equal to
  44. 44The solution set of x ∈ - π , π for the inequality sin ⁡ 2 x + 1 ≤ cos ⁡ x + 2 sin ⁡ x is
  45. 45If α and β are the solutions of cot ⁡ x = - 3 in 0,2 π and α and γ are the solutions of cosec ⁡ x = - 2 in 0,2 π , then the value of α - β β
  46. 46If sin ⁡ x + cos ⁡ x = 7 2 , where x ∈ 0 , π 4 , then the value of t a n x 2 is equal to
  47. 47The number of roots of the equation tan ⁡ x + sec ⁡ x =2 cos ⁡ x in 0 , 4 π is
  48. 48If x = 2 n + t a n - 1 p q and y = r is a solution of the equation 12 sin x + 5 cos x = 2 y 2 - 8 y + 21 , then the value of k , such that p
  49. 49The equation k cos ⁡ x - 3 sin ⁡ x = k + 1 is solvable only if
  50. 50If sin ⁡ 2 A = 1 2 and sin ⁡ 2 B = - 1 2 , then which of the following is false?

Frequently Asked Questions

1.How many questions are available for Trigonometric Equations?

This chapter includes 83 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 Equations 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 Equations questions in NTA Abhyas (JEE Main)?

Of the 83 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 Equations should I focus on?

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