Trigonometric Ratios & Identities: JEE Main Mathematics Previous Year Questions

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

1. 1.In a $\text{△}\text{ABC}$, with usual notation, if $a=12\text{,}b=16$ and $c=20$, then the ratio of the exradii of the triangle opposite to the angles in the order…
2. 2.…
3. 3.In $\text{△}\text{ABC}$, if $A$ is an acute angle, $b=6\text{,}c=9$ and $\text{sin}\text{⁡}A=\frac{2\sqrt{14}}{9}$, then…
4. 4.If $\text{△}\text{ABC}$ is such that $\text{∠}A={90}^{\circ }\text{,}\text{∠}B\ne \text{∠}C$, then…
5. 5.If $(\text{sin}\text{⁡}x-{\text{cos}}^2\text{⁡}x)\ge (3-3\text{sin}\text{⁡}x+{\text{sin}}^2\text{⁡}x)+4\text{|}\text{sin}\text{⁡}x-1\text{|}$, then $x=$
6. 6.Let S = $(x\text{∈}\text{(}-\pi \text{,}\pi \text{)}\text{:}x\ne 0\text{,}\pm \frac{\pi }{2})$The sum of all distinct solutions of the equation $\sqrt{3}$sec x…
7. 7.If $f\text{(}x\text{)}=\frac{{\text{cos}}^2\text{⁡}x+{\text{sin}}^4\text{⁡}x}{{\text{sin}}^2\text{⁡}x+{\text{cos}}^4\text{⁡}x}\text{∀}x\text{∈}R$, then…
8. 8.If $\text{sin}\text{⁡}\text{(}A+B\text{)}\text{sin}\text{⁡}\text{(}A-B\text{)}+\text{cos}\text{⁡}\text{(}A+B\text{)}\text{cos}\text{⁡}\text{(}A-B\text{)}=\frac{1}{2}$ an…
9. 9.If $a=2\text{,}b=3\text{,}c=4$ in a triangle $\text{ABC}$, then $\text{cos}\text{⁡}C=$
10. 10.$2{\text{cos}}^{-1}\text{⁡}x={\text{sin}}^{-1}\text{⁡}\left(2x\sqrt{1-x^2}\right)$ is valid for all values of $x$ satisfying
11. 11.The period of…
12. 12.The value of cos…
13. 13.The value of…
14. 14.…
15. 15.The number of integral values of $k$ for which the equation $7\text{cos}\text{⁡}x+5\text{sin}\text{⁡}x=2k+1$ has a solution, is
16. 16.$\frac{1}{\text{cos}\text{⁡}{290}^{\circ }}+\frac{1}{\sqrt{3}\text{sin}\text{⁡}{250}^{\circ }}=$
17. 17.If $\text{cos}\text{⁡}\theta -\text{sin}\text{⁡}\theta =\sqrt{5}\text{sin}\text{⁡}\theta$, then $\text{cos}\text{⁡}\theta +4\text{sin}\text{⁡}\theta =$
18. 18.In a $\text{△}\text{ABC}$, with usual notation, if $r=r_1-r_2-r_3$, then $2R=$
19. 19.If $e^{({\text{cos}}^2\text{⁡}x+{\text{cos}}^4\text{⁡}x+{\text{cos}}^6\text{⁡}x+\text{…}\infty ){\text{log}}_e\text{⁡}2}$ satisfies the equation…
20. 20.The number of integral values of $\text{’}k\text{’}$ for which the equation $3\text{sin}\text{⁡}x+4\text{cos}\text{⁡}x=k+1$ has a solution, $k\text{∈}R$ is
21. 21.If $\text{sin}\text{⁡}\text{hx}=\text{tan}\text{⁡}A$, then $\text{|}\text{tan}\text{⁡}\text{hx}\text{|}=$
22. 22.If $\text{sinh}\text{⁡}u=\text{tan}\text{⁡}\theta$, then $\text{cosh}\text{⁡}u$ is equal to
23. 23.If $\text{tan}\text{⁡}A=\frac{1}{\sqrt{x(x^2+x+1)}}\text{,}\text{tan}\text{⁡}B=\frac{\sqrt{x}}{\sqrt{x^2+x+1}}$ and…
24. 24.If…
25. 25.The range of the function,…