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Important Questions: Trigonometry for JEE

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The most important Trigonometry questions for JEE cover conceptual traps, standard results, and numerical patterns from Trigonometrical identities and trigonometrical functions, Inverse trigonometrical functions and their properties. Goodmarks provides 46+ high-yield MCQs with full solutions.

Focus on what matters most. These important Trigonometry questions cover high-weightage concepts from Trigonometrical identities and trigonometrical functions, Inverse trigonometrical functions and their properties — the topics JEE repeats every year.

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Q1MathsUnit 14: Trigonometry

Assertion Consider

\boldsymbol{f}(\boldsymbol{x})=\sin ^{-1}\left(\sec \left(\tan ^{-1} \boldsymbol{x}\right)+\right.

\cos ^{-1}\left(\operatorname{cosec}\left(\cot ^{-1} x\right)\right.

Statement-1: Domain of

f(x)

is a singleton. Reason Statement-2: Range of the function

\boldsymbol{f}(\boldsymbol{x})

is a singleton.

Q2MathsUnit 14: Trigonometry

The number of real solutions of the equation

\tan ^{-1} \sqrt{x(x+1)}+

\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{2}

Q3MathsUnit 14: Trigonometry

\mathbf{A}=\cos 20^{0} \cos 40^{0} \cos 60^{0} \cos 80^{0}

\mathbf{B}=\cos 6^{0} \cos 42^{0} \cos 66^{0} \cos 78^{0}

\mathbf{C}=\cos \mathbf{3} \mathbf{6}^{\mathbf{0}} \cos \mathbf{7} \mathbf{2}^{\mathbf{0}} \cos \mathbf{1 0} \mathbf{8}^{\mathbf{0}} \cos \mathbf{1} \mathbf{4} \mathbf{4}^{\mathbf{0}}

Q4MathsUnit 14: Trigonometry

The measures of the angles of a triangle are in the ratio

4: 5: 9 .

The triangle is:

Q5MathsUnit 14: Trigonometry

If value of

\mathbf{x}

which satisfy equation

\left(\cot ^{-1} x\right)^{2}-3\left(\cot ^{-1} x\right)+2>0

x<

\cot a

x>\cot b

Find the value of

a+b

Q6MathsUnit 14: Trigonometry

\ln \Delta A B C, B C=A B

and

\angle B=80^{\circ}

Then

\angle A

is equal to

Q7MathsUnit 14: Trigonometry

Two line segments

A B

and

A C

include an angle of

60^{0}

where

A B=5 \mathrm{cm}

and

A C

=7 \mathrm{cm} .

Locate points

\mathrm{P}

and

\mathrm{Q}

\mathrm{AB}

and

A C,

respectively such that

A P=\frac{3}{4}

A B

and

A Q=\frac{1}{4} A C .

Join

P

and

Q

and measure the length PQ.

Q8MathsUnit 14: Trigonometry

Statement I: The equation

\left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}-a \pi^{3}=0

has solution for all

a \geqslant \frac{1}{32}

Statement II : For any

\boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \boldsymbol{s} \boldsymbol{i n}^{-1} \boldsymbol{x}+

\cos ^{-1} x=\frac{\pi}{2}

and

0 \leq\left(\sin ^{-1} x-\frac{\pi}{4}\right)^{2} \leq

\frac{9 \pi^{2}}{16}

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Frequently asked questions

What makes a Trigonometry question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Trigonometry are high-weightage?

Key areas include Trigonometrical identities and trigonometrical functions, Inverse trigonometrical functions and their properties. Prioritise these before moving to edge cases.

How many important questions should I revise?

Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

Can I practise only important questions on Goodmarks?

Pro users can filter by unit and subtopic to target high-yield areas. Free users can attempt sample questions on this page.