JEE Main Maths Inverse Trigonometric Functions Previous Year Questions

JEE Main Inverse Trigonometric Functions PYQ, free to download as a 42-page PDF. The bank carries 27 solved questions from the 2023 to 2026 papers and takes roughly two days to work through, so split it across identities and domains.

Every question keeps the year it was asked and the options exactly as printed. An answer key follows the questions, then a full worked solution for all 27.

How the Answers Were Checked

These questions come from our tagged JEE Main bank, which ships an answer key. That key was not taken on trust.

Every one of the 27 answers was independently re-derived from the question itself, both symbolically and numerically, before publication. All 27 agreed with the bank.

One further question was set aside. It was a multiple-answer type whose two correct options turn out to be the same value written differently, which a single-answer booklet cannot represent honestly.

What the 27 Questions Cover

Inverse trigonometry is a compact chapter that JEE Main returns to every year, and the recent papers lean heavily on domains rather than pure identity manipulation.

• Domain and range, where two or three conditions must be intersected, now the most common style
• Addition formulae for inverse tangents, including when the formula needs a correction term
• Principal values, where an angle outside the principal range must be reduced correctly
• Telescoping series, both finite and infinite
• Identity collapses, where a long expression reduces to a constant
• Counting solutions, where extraneous roots have to be discarded

The Five Moves That Solve Almost All of Them

Across the 27 questions the same handful of moves keeps working. Naming them makes the chapter much faster.

• Convert every inverse function to a tangent before combining; mixing sine and cosine forms is what makes expressions look hard
• Remember that inverse sine plus inverse cosine of the same argument is always a right angle, which collapses many expressions instantly
• For domains, solve the tightest condition first, then check the others only on that interval
• After using an addition formula, always substitute the root back; the formula introduces solutions that do not satisfy the original equation
• Reduce an out-of-range angle into each function's own principal range separately, since they differ

Two Questions Worth Doing First

If time is short, start here. Each teaches a move the rest of the set reuses.

2023, the empty solution set. An equation is posed on a closed interval and the answer is that no value satisfies it, so the required sum is over nothing at all. Bounding both sides before solving shows in two lines that the equation asks for more than the ranges permit.

2025, the infinite telescoping series. The numerators 7, 19, 39 and 67 have constant second differences, which fixes the general term. Only then does the telescoping split reveal itself, and guessing the pattern from the first two terms gives the wrong sequence entirely.

Watch Inverse Trigonometric Functions Solved for JEE Main

Source: JEE Wallah

How to Use the Answer Key and Solutions

Attempt the whole set before checking anything. The layout is built so an answer cannot be glimpsed by accident.

• Do the set in two timed sittings, allowing about three minutes a question
• Mark the answer key in one pass, right or wrong only
• Read the solution for every miss and every lucky guess
• Each solution opens with a one-line quick solution, so you can stop there and retry

Traps These Questions Are Built Around

A handful of errors account for most lost marks here, and several questions exist only to catch them.

• Applying the inverse tangent addition formula without checking whether a correction term is needed
• Cancelling the inverse function without confirming the angle sits in its principal range
• Reducing an out-of-range angle the same way for inverse sine and inverse cosine, whose ranges differ
• Dividing by a factor that the interval does not guarantee is non-zero
• Reading a general term from the first two values instead of from the second differences

For the rest of the paper, the JEE Main Ellipse and Hyperbola PYQs cover conic sections in the same format.