Mathematics — Trigonometry for the JEE Main Exam

Common failure modes

These are the patterns that cause most candidates to lose marks on this topic. Recognising them in advance is half the work.

• !Forgetting the domain and range of arcsin (−π/2 to π/2) vs arccos (0 to π)
• !Applying sum-to-product formulas incorrectly when signs differ (sin A − sin B ≠ sin(A−B))
• !Missing multiple solutions of trigonometric equations by not writing the general solution
• !Confusing the law of sines (a/sin A) with the law of cosines — choosing the wrong formula for the given data

Study tips

• 1Memorise the transformation identities (sum-to-product, product-to-sum) — they appear in definite integral evaluations as well as pure trigonometry questions.
• 2For inverse trig, drill the composition identities: sin(arccos x) = √(1−x²), arcsin(x) + arccos(x) = π/2, and the double-angle inverses.
• 3Write the general solution for trigonometric equations every time: sin θ = k → θ = nπ + (−1)ⁿ arcsin k. JEE marks are lost by giving only one particular solution.
• 4Practice properties-of-triangles (sine rule, cosine rule, area formula) timed at 2 minutes per problem.

Sample JEE Main Mathematics — Trigonometry questions

These sample items mirror the format and difficulty of real JEE Main questions. Practice with thousands more on the free Koydo question bank.

1. 1

   The principal value of arcsin(−1/2) is:

   • A−π/6Correct
   • Bπ/6
   • C−π/3
   • D5π/6
   Why this answer?

   Illustrative JEE-style: sin(−π/6) = −1/2, and −π/6 lies in the principal range [−π/2, π/2]. Therefore arcsin(−1/2) = −π/6.

2. 2

   If sin A + sin B = x and cos A + cos B = y, then tan((A+B)/2) equals:

   • Ax/yCorrect
   • By/x
   • C(x+y)/(x−y)
   • D(x−y)/(x+y)
   Why this answer?

   Illustrative JEE-style: Using sum-to-product: sin A + sin B = 2 sin((A+B)/2) cos((A−B)/2) = x, and cos A + cos B = 2 cos((A+B)/2) cos((A−B)/2) = y. Dividing gives tan((A+B)/2) = x/y.

3. 3

   In a triangle, if a = 2, b = 3, and C = 60°, the value of side c (by the cosine rule) is:

   • A√7Correct
   • B√13
   • C√5
   • D√19
   Why this answer?

   Illustrative JEE-style: c² = a² + b² − 2ab cos C = 4 + 9 − 2(2)(3)(1/2) = 13 − 6 = 7. So c = √7.