Trigonometric Equations: JEE Main Mathematics Previous Year Questions

47 previous year questions from Trigonometric Equations. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.A value of $\theta \in \left(0,\frac{\pi }{3}\right)$, for which…
2. 2.The number of solutions for the equation $\text{sin}\text{⁡}2x+\text{cos}\text{⁡}4x=2$ is
3. 3.The general solution of $\text{cot}\text{⁡}\theta +\text{tan}\text{⁡}\theta =2$ is
4. 4.If $\alpha \text{,}-\frac{\pi }{2}<\alpha <\frac{\pi }{2}$ is the solution of $4\text{cos}\text{⁡}\theta +5\text{sin}\text{⁡}\theta =1$, then the value of…
5. 5.Let…
6. 6.The sum of all values of $\theta \text{∈}\text{[}0\text{,}2\pi \text{]}$ satisfying $2{\text{sin}}^2\theta =\text{cos}2\theta$ and…
7. 7.The number of solutions of $si{n}^7$ x + $co{s}^7$ x = 1 x ∈ [0, 4π], is equal to
8. 8.The general solution of $\text{|}\text{sin}\text{⁡}x\text{|}=\text{cos}\text{⁡}x$ is (when $n\text{∈}Z$ ) given by
9. 9.Let $f\left(\theta \right)=3({\text{sin}}^4(\frac{\pi }{2}-\theta )+{\text{sin}}^4(3\pi +\theta ))-2(1-{\text{sin}}^{2}2\theta )$ and…
10. 10.The number of elements in the set…
11. 11.Suppose $\theta ϵ\left(0\text{,}\frac{\pi }{4}\right)$ is a solution of $4\text{cos}\text{⁡}\theta -3\text{sin}\text{⁡}\theta =1$. Then $\text{cos}\text{⁡}\theta$ is…
12. 12.Let the set of all $a\text{∈}R$ such that the equation $\text{cos}\text{⁡}2x+a\text{sin}\text{⁡}x=2a-7$ has a solution be $\text{[}p\text{,}q\text{]}$ and…
13. 13.Number of solutions of $\sqrt{3}\text{cos}2\theta +8\text{cosθ}+3\sqrt{3}=0\text{,}\theta \text{∈}\text{[}-3\pi \text{,}2\pi \text{]}$ is:
14. 14.If $0\le x<\frac{\pi }{2}$, then the number of values of x for which $\text{sin}x-\text{sin}2x+\text{sin}3x=0$, is;
15. 15.The number of solutions of the equation$\text{|}\text{cot}\text{⁡}x\text{|}=\text{cot}\text{⁡}x+\frac{1}{\text{sin}x}$in the interval$\text{[}0\text{,}2\pi \text{]}$ is
16. 16.The general solution of $1+{\text{sin}}^2\text{⁡}x=3\text{sin}\text{⁡}x\cdot \text{cos}\text{⁡}x$, $\text{tan}\text{⁡}x\ne \frac{1}{2}$ is
17. 17.The sum of the solutions $x\text{∈}R$ of the equation…
18. 18.All the pairs $(x,y)$ that satisfy the inequality $2^{\sqrt{{\sin }^{2}x-2\sin x+5}}\cdot \frac{1}{4^{{\sin }^{2}y}}\le 1$ also satisfy the equation:
19. 19.If $\text{cos}\text{⁡}x=\text{|}\text{sin}\text{⁡}x\text{|}$, then the general solution is
20. 20.If the equation ${\text{cos}}^4\text{⁡}\theta +{\text{sin}}^4\text{⁡}\theta +\lambda =0$has real solutions for $\theta$, then $\lambda$ lies in the interval
21. 21.The sum of all values of $\theta \text{∈}\left(0\text{,}\frac{\pi }{2}\right)$ satisfying ${\text{sin}}^{2}2\theta +{\text{cos}}^{4}2\theta =\frac{3}{4}$ is:
22. 22.If $2{\text{sin}}^3\text{⁡}x+\text{sin}\text{⁡}2x\text{cos}\text{⁡}x+4\text{sin}\text{⁡}x-4=0$ has exactly 3 solutions in the interval…
23. 23.The number of solutions of the equation…
24. 24.If $2{\text{tan}}^2\text{⁡}\theta -5\text{sec}\text{⁡}\theta =1$ has exactly 7 solutions in the interval $\left(0\text{,}\frac{\text{nπ}}{2}\right)$, for the least va…
25. 25.Let S be the set of all $\alpha \text{∈}R$ such that the equation, $\text{cos}2x+\alpha \text{sin}x=2\alpha -7$ has a solution. Then S is equal to :