Trigonometry JEE Main Practice Test 2026 | Important Questions with Answers

Trigonometry – JEE Main Practice Test

This Trigonometry JEE Main Practice Test contains the most important and repeated questions asked in JEE Main from inverse trigonometry and trigonometric ratios. Practising these questions improves accuracy and confidence for the actual exam.

Q1. The domain of the function f(x) = sin⁻¹((x² − 3x + 2)/(x² + 2x + 7)) is:

[1, ∞)

[−1, 2]

[−1, ∞)

(−∞, 2]

Q2. For n ∈ N, if cot⁻¹3 + cot⁻¹4 + cot⁻¹5 + cot⁻¹n = π, then n is equal to:

Correct Answer: 47

Q3. The value of cos(2π/7) + cos(4π/7) + cos(6π/7) is:

−1

−1/2

−1/3

−1/4

Q4. For x ∈ (−1,1), the number of solutions of sin⁻¹x = 2tan⁻¹x is:

Correct Answer: 2

Q5. The set of all values of λ for which cos²2x − 2sin⁴x − 2cos²x = λ has a real solution is:

[−2, −1]

[−3/2, −1]

[−2, −3/2]

[−1, −1/2]

Q6. If the equation cos⁴θ + sin⁴θ + λ = 0 has real solutions, then λ lies in:

[−3/2, −5/4]

(−1/2, −1/4]

(−5/4, −1]

[−1, −1/2]

Q7. If 5(tan²x − cos²x) = 2cos2x + 9, then the value of cos4x is:

1/3

2/9

−7/9

−3/5

Q8. If 10sin⁴θ + 15cos⁴θ = 6, then the value of (27cosec⁶θ + 8sec⁶θ)/(16sec⁸θ) is:

2/5

3/5

1/5

3/4

Q9. The value of cos(sin⁻¹(3/5) + sin⁻¹(5/13) + sin⁻¹(33/65)) is:

33/65

32/65

Q10. The domain of the function f(x) = cos⁻¹((x² − 5x + 6)/(x² − 9)) / ln(x² − 3x + 2) is:

(−∞,1) ∪ (2,∞)

(2,∞)

[−1/2,1) ∪ (2,∞)

[−1/2,1) ∪ (2,∞) − {3,(3±√5)/2}

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About this JEE Main Practice Test

Designed strictly for JEE Main level
Concept-based + exam-oriented questions
Improves speed, accuracy and confidence
High relevance for JEE Main 2026