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Trigonometric Identities

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 7 times: 2021 Paper 19, 26 Jun 2022, 25 Jul 2022, 8 Apr 2023, 10 Apr 2023, 24 Jan 2026 S1, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 7 of this type

    61
    If sin⁡(π18)sin⁡(5π18)sin⁡(7π18)=K\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⁡(10Kπ3)\sin\left( \frac{10K\pi}{3} \right) is :

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  2. Question 2

    This type asked 5 times: 2021 Paper 22, 25 Jun 2022, 27 Jun 2022, 8 Apr 2024, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 5 of this type

    74
    If cos⁡248∘−sin⁡212∘sin⁡224∘−sin⁡26∘=α+β52\frac{\cos^{2}48^{\circ} - \sin^{2}12^{\circ}}{\sin^{2}24^{\circ} - \sin^{2}6^{\circ}} = \frac{\alpha + \beta\sqrt{5}}{2}, where α,β∈N\alpha,\beta \in \mathbb{N}, then α+β\alpha + \beta is equal to ____\_\_\_\_ .

  3. Question 3

    This type asked 3 times: 2021 Paper 17, 9 Apr 2024, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 3 of this type

    63
    The least value of (cos⁡2θ−6sin⁡θcos⁡θ+3sin⁡2θ+2)\left( \cos^{2}\theta - 6\sin\theta \cos\theta + 3\sin^{2}\theta + 2 \right) is

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  4. Question 4

    Asked 2 times: 23 Jan 2026 S2*, 24 Jan 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    60
    If cot⁡x=512\cot x =\frac{5}{12} for some x∈(π,3π2)x \in\left( \pi,\frac{3\pi}{2} \right), then sin⁡7x(cos⁡13x2+sin⁡13x2)+cos⁡7x(cos⁡13x2−sin⁡13x2)\sin7x\left( \cos\frac{13x}{2}+ \sin\frac{13x}{2} \right)+ \cos7x\left( \cos\frac{13x}{2}- \sin\frac{13x}{2} \right) is equal to

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  5. Question 5

    Asked 2 times: 2021 Paper 10*, 4 Apr 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    70
    If 10sin⁡4θ+15cos⁡4θ=610\sin^{4}\theta+ 15\cos^{4}\theta= 6, then the value of 27csc⁡6θ+8sec⁡6θ16sec⁡8θ\frac{27\csc^{6}\theta+ 8\sec^{6}\theta}{16\sec^{8}\theta} is:

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  6. Question 6

    This type asked 2 times: 28 Jan 2025, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 2 of this type

    73
    If A=sin⁡3∘cos⁡9∘+sin⁡9∘cos⁡27∘+sin⁡27∘cos⁡81∘A = \frac{\sin 3^{\circ}}{\cos 9^{\circ}} + \frac{\sin 9^{\circ}}{\cos 27^{\circ}} + \frac{\sin 27^{\circ}}{\cos 81^{\circ}} and B=tan⁡81∘−tan⁡3∘B = \tan81^{\circ} - \tan3^{\circ}, then BA\frac{B}{A} is equal to ____\_\_\_\_ .

  7. Question 7

    This type asked 2 times: 28 Jun 2022, 8 Apr 2024. This one: 8 Apr 2024 See all 2 of this type

    71
    If sin⁡x=−35\sin x= -\frac{3}{5}, where π<x<3π2\pi<x<\frac{3\pi}{2}, then 80(tan⁡2x−cos⁡x)80\left( \tan^{2}x- \cos x \right) is equal to:

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  8. Question 8

    This type asked 2 times: 2021 Paper 5, 2021 Paper 16. This one: 2021 Paper 16 See all 2 of this type

    47
    If sin⁡θ+cos⁡θ=12\sin\theta+ \cos\theta=\frac{1}{2}, then 16[sin⁡2θ+cos⁡4θ+sin⁡6θ]16\lbrack \sin2\theta+ \cos4\theta+ \sin6\theta\rbrack is equal to

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  9. Question 9

    Asked once: 24 Jan 2026 S1 (same type asked 7 times) See all 7 of this type

    58
    The value of 3csc⁡20∘−sec⁡20∘cos⁡20∘cos⁡40∘cos⁡60∘cos⁡80∘\frac{\sqrt{3}\csc20^{\circ}- \sec20^{\circ}}{\cos20^{\circ}\cos40^{\circ}\cos60^{\circ}\cos80^{\circ}} is equal to

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  10. Question 10

    Asked once: 8 Apr 2024 (same type asked 5 times) See all 5 of this type

    159
    If the value of 3cos⁡36∘+5sin⁡18∘5cos⁡36∘−3sin⁡18∘\frac{3\cos36^{\circ}+ 5\sin18^{\circ}}{5\cos36^{\circ}- 3\sin18^{\circ}} is a5−bc\frac{a\sqrt{5}-b}{c}, where a,b,ca,b,c are natural numbers and gcd⁡(a,c)=1\gcd(a,c) = 1, then a+b+ca + b + c is equal to:

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