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JEE Advanced Trigonometry and Inverse Trigonometric Functions questions with solutions

Trigonometric ratios, identities, equations, inverse trigonometric functions and properties of triangles. 18 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 11 and 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Trigonometry and Inverse Trigonometric Functions for JEE Main

JEE Advanced 2025

Let S be the sum of all solutions of sin x+sin 2x+sin 3x=cos x+cos 2x+cos 3x in the interval [0,2π]. If S=kπ, find k.JEE Advanced 2025 Paper 2 · medium

JEE Advanced 2024

The number of solutions of the equation sin x+sin 3x+sin 5x=cos x+cos 3x+cos 5x in the interval [0,2π] is ______.JEE Advanced 2024 Paper 1 · medium
Let S=Σk=1^∞tan ^-1 ((2)/(k^2), where tan ^-1 takes values in (-(π)/(2),(π)/(2)). The value of (4S)/(π) is ______.JEE Advanced 2024 Paper 1 · hard

JEE Advanced 2022

In a triangle ABC the side lengths a,b,c are in arithmetic progression, the perimeter is 30, and the largest angle is 120^°. Let O and I be the…JEE Advanced 2022 Paper 1 · medium
Consider the equation sin x+sin 2x+sin 3x=cos x+cos 2x+cos 3x for x∈[0,2π].JEE Advanced 2022 Paper 1 · medium
The number of values of x∈[0,2π] for which sin x+sin 2x+sin 3x=0 but cos x+cos 2x+cos 3x≠0 isJEE Advanced 2022 Paper 2 · medium
Let Sn=Σk=1^ntan ^-1 ((2)/(k^2). Then lim n→∞n((3π)/(4)-Sn) equalsJEE Advanced 2022 Paper 2 · hard

JEE Advanced 2021

In a triangle ABC the sides are BC=4, CA=5 and AB=6.JEE Advanced 2021 Paper 1 · medium
Find the number of values of x∈[0,2π] satisfying sin x+sin 2x+sin 3x=cos x+cos 2x+cos 3x.JEE Advanced 2021 Paper 2 · medium

JEE Advanced 2020

Consider the equation sin x+sin 2x+sin 3x=0 for x∈[0,2π].JEE Advanced 2020 Paper 1 · medium
For a positive integer N let SN=Σn=1^Ntan ^-1 ((2)/(n^2) and let S=lim N→∞SN.JEE Advanced 2020 Paper 2 · hard
In a triangle ABC, AB=5, AC=8 and ∠ A=60^°. Let O and I be the circumcentre and the incentre of the triangle. Find the distance OI.JEE Advanced 2020 Paper 2 · hard

JEE Advanced 2019

In an acute-angled triangle ABC, tan A=2 and tan B=3, and the circumradius is R=√(10). Let a,b,c be the sides opposite to A,B,C.JEE Advanced 2019 Paper 1 · medium

JEE Advanced 2018

Let S be the set of all x∈[0,2π] satisfying sin x+sin 2x+sin 3x=cos x+cos 2x+cos 3x. Find the sum of all elements of S divided by π.JEE Advanced 2018 Paper 1 · medium
Let tk=tan ^2(kπ)/(7) for k=1,2,3. Find the value of (t1+t2+t3)+t1t2t3.JEE Advanced 2018 Paper 2 · hard

JEE Advanced 2017

Find the number of solutions of sin x+sin 2x+sin 3x=cos x+cos 2x+cos 3x in the interval [0,2π].JEE Advanced 2017 Paper 1 · easy

JEE Advanced 2016

Consider the equation tan x+tan 2x+tan 3x=tan x tan 2x tan 3x for x∈(0,π) at which all the tangents are defined.JEE Advanced 2016 Paper 1 · medium
Consider the equation sin x+sin 2x+sin 3x=0.JEE Advanced 2016 Paper 2 · medium

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Differentiation and Application of Derivatives 20 Indefinite and Definite Integrals 18 Limits 19 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Quadratic Equations 12 Sequences and Series 11 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Vector Algebra 9