Trigonometric Ratios & Identities JEE Main PYQs PDF, 2020–2026

Trigonometric Ratios & Identities questions per year

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 63 of the 85 asked.

Topic-wise weightage by year

How many Trigonometric Ratios & Identities questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 14 JEE Main 2026 Trigonometric Ratios & Identities questions in the free PDF, latest shift first.

1. JEE Main 2026 · 5 Apr · Shift 1 · Compound Angle Formulas

   Let $\tan A,\tan B$, where $A,B\in \left(-\frac{\pi}{2},\frac{\pi}{2}\right)$, be the roots of the quadratic equation $x^{2}-2x-5=0$. Then $20\sin^{2}\left(\frac{A+B}{2}\right)$ is equal to:

   Solve it online →

2. JEE Main 2026 · 4 Apr · Shift 1 · Product-to-Sum and Sum-to-Product

   If ${\mathrm{A}}=\frac{\sin 3^{{\circ}}}{\cos 9^{{\circ}}}+\frac{\sin 9^{{\circ}}}{\cos {27}^{{\circ}}}+\frac{\sin {27}^{{\circ}}}{\cos {81}^{{\circ}}}$ and ${\mathrm{B}}=\tan {81}^{{\circ}}-\tan 3^{{\circ}}$, then $\frac{{\mathrm{B}}}{{\mathrm{A}}}$ is equal to

   $\_\_\_\_$ .

   Solve it online →

3. JEE Main 2026 · 4 Apr · Shift 1 · Product-to-Sum and Sum-to-Product

   Let $\overrightarrow{a_{k}}=(\tan \theta_{k}){\hat{i}}+{\hat{j}}$ and $\overrightarrow{b_{k}}={\hat{i}}-(\cot \theta_{k}){\hat{j}}$, where $\theta_{k}=\frac{2^{{k-1}}\pi}{2^{n}+1}$, for some $n\in {\mathbb{N}},n>5$. Then the value of $\frac{\sum_{{k=1}}^{n}\left|\overrightarrow{a_{k}}\right|^{2}}{\sum_{{k=1}}^{n}\left|\overrightarrow{b_{k}}\right|^{2}}$ is

   Solve it online →

4. JEE Main 2026 · 2 Apr · Shift 2 · Multiple and Sub-Multiple Angles

   Let $P=\{\theta\in [0,4\pi]:\tan^{2}\theta\neq 1\}$ and $S=\{a\in {\mathbb{Z}}:2(\cos^{8}\theta-\sin^{8}\theta)\sec 2\theta=a^{2},\theta\in P\}$. Then $n(S)$ is:

   Solve it online →

5. JEE Main 2026 · 2 Apr · Shift 1 · Multiple and Sub-Multiple Angles

   If $\sin \left(\frac{\pi}{18}\right)\sin \left(\frac{5\pi}{18}\right)\sin \left(\frac{7\pi}{18}\right)=K$, then the value of $\sin \left(\frac{10K\pi}{3}\right)$ is:

   Solve it online →

6. JEE Main 2026 · 28 Jan · Shift 1 · Compound Angle Formulas

   If $\frac{\tan ({\mathrm{A}}-{\mathrm{B}})}{\tan {\mathrm{A}}}+\frac{\sin^{2}{\mathrm{C}}}{\sin^{2}{\ \mathrm{A}}}=1,{\ \mathrm{A}},{\ \mathrm{B}},{\mathrm{C}}\in \left(0,\frac{\pi}{2}\right)$, then

   Solve it online →

7. JEE Main 2026 · 24 Jan · Shift 1 · Multiple and Sub-Multiple Angles

   If $\cot x=\frac{5}{12}$ for some $x\in \left(\pi,\frac{3\pi}{2}\right)$, then $\sin 7x\left(\cos \frac{13x}{2}+\sin \frac{13x}{2}\right)+\cos 7x\left(\cos \frac{13x}{2}-\sin \frac{13x}{2}\right)$ is equal to

   Solve it online →

8. JEE Main 2026 · 24 Jan · Shift 1 · Multiple and Sub-Multiple Angles

   The value of $\frac{\sqrt{3}\operatorname{cosec}{20}^{{\circ}}-\sec {20}^{{\circ}}}{\cos {20}^{{\circ}}\cos {40}^{{\circ}}\cos {60}^{{\circ}}\cos {80}^{{\circ}}}$ is equal to

   Solve it online →

9. JEE Main 2026 · 23 Jan · Shift 1 · Maximum and Minimum Values

   Let $\alpha$ and $\beta$ respectively be the maximum and the minimum values of the function $f(\theta)=4\left(\sin^{4}\left(\frac{7\pi}{2}-\theta\right)+\sin^{4}(11\pi+\theta)\right)-2\left(\sin^{6}\left(\frac{3\pi}{2}-\theta\right)+\sin^{6}(9\pi-\theta)\right),\theta\in {\mathbf{R}}$.

   Then $\alpha+2\beta$ is equal to :

   Solve it online →

10. JEE Main 2026 · 23 Jan · Shift 2 · Maximum and Minimum Values

    The least value of $\left(\cos^{2}\theta-6\sin \theta\cos \theta+3\sin^{2}\theta+2\right)$ is

    Solve it online →

11. JEE Main 2026 · 23 Jan · Shift 2 · Multiple and Sub-Multiple Angles

    Let $\frac{\pi}{2}<\theta<\pi$ and $\cot \theta=-\frac{1}{2\sqrt{2}}$. Then the value of

    $\sin \left(\frac{15\theta}{2}\right)(\cos 8\theta+\sin 8\theta)+\cos \left(\frac{15\theta}{2}\right)(\cos 8\theta-\sin 8\theta)$

    is equal to :

    Solve it online →

12. JEE Main 2026 · 22 Jan · Shift 2 · Multiple and Sub-Multiple Angles

    Let $\cos (\alpha+\beta)=-\frac{1}{10}$ and $\sin (\alpha-\beta)=\frac{3}{8}$, where $0<\alpha<\frac{\pi}{3}$ and $0<\beta<\frac{\pi}{4}$. If $\tan 2\alpha=\frac{3(1-r\sqrt{5})}{\sqrt{11}(s+\sqrt{5})},r,s\in N$, then $r+s$ is equal to $\_\_\_\_$ .

    Solve it online →

Practise the 2026 Trigonometric Ratios & Identities questions online

Sample questions from recent papers

The free PDF above has all 63 questions grouped by topic, with an answer key.

Frequently asked

More Mathematics chapters

• Applications of Derivatives (156 asked · 153 in PDF)
• Area Under Curves (138 asked · 136 in PDF)
• Binomial Theorem (197 asked · 196 in PDF)
• Circles (117 asked · all in PDF)
• Complex Numbers (162 asked · 161 in PDF)
• Continuity & Differentiability (94 asked · all in PDF)
• Definite Integration (225 asked · 223 in PDF)
• Determinants (188 asked · all in PDF)
• Differential Equations (204 asked · 202 in PDF)
• Differentiation (38 asked · all in PDF)
• Ellipse (100 asked · all in PDF)
• Functions (Advanced) (71 asked · all in PDF)
• Hyperbola (63 asked · 62 in PDF)
• Indefinite Integration (60 asked · all in PDF)
• Inverse Trigonometric Functions (94 asked · all in PDF)
• Limits (110 asked · all in PDF)
• Matrices (111 asked · all in PDF)
• Parabola (107 asked · 104 in PDF)
• Permutations & Combinations (163 asked · 162 in PDF)
• Probability: Advanced (97 asked · all in PDF)
• Probability: Basic (79 asked · 78 in PDF)
• Quadratic Equations & Polynomial Inequalities (129 asked · 128 in PDF)
• Relations & Functions (Basic) (139 asked · 137 in PDF)
• Sequences & Series (247 asked · 246 in PDF)
• Sets (39 asked · all in PDF)
• Statistics (104 asked · all in PDF)
• Straight Lines (130 asked · 123 in PDF)
• Three Dimensional Geometry (297 asked · all in PDF)
• Trigonometric Equations (48 asked · all in PDF)
• Vectors (216 asked · 212 in PDF)

JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020