\(\text{The value of } cosec20°tan60°-sec20° \text{is }\)
\(0\)
\(1\)
\(2\)
\(4\)
\(6\)
The Correct Option is D
Solution and Explanation
\(cosec20.tan60-sec20\)
\(=\dfrac{1}{sin20}×\dfrac{sin60}{cos60}-\dfrac{1}{cos20}\)
\(=\dfrac{sin60.cos20-cos60.sin20}{sin20.cos60.cos20}\)
\(=\dfrac{sin(60-20)}{\dfrac{1}{2}.sin20.cos20}\)
\(=\dfrac{2.sin40}{sin20.cos20}\)
\(=\dfrac{2sin2(20)}{sin20.cos20}\)
\(=\dfrac{4sin20.cos20}{sin20.cos20}\)
\(=4\) (_Ans)
Top Questions on Trigonometry
- Number of solutions in the interval \( [-2\pi, 2\pi] \) for the equation: \[ 2\sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0 \]
- JEE Main - 2025
- Mathematics
- Trigonometry
- Let \( S = \{ x : \cos^{-1} x = \pi + \sin^{-1} x + \sin^{-1} (2x + 1) \ \). Then \[ \sum_{x \in S} (2x - 1)^2 \text{ is equal to:} \]
- JEE Main - 2025
- Mathematics
- Trigonometry
- If \[ \sum_{r=1}^{13} \frac{1}{\sin \frac{\pi}{4} + (r-1) \frac{\pi}{6}} \sin \frac{\pi}{4} + \frac{\pi}{6} = a \sqrt{3} + b, \quad a, b \in \mathbb{Z}, { then } a^2 + b^2 { is equal to:} \]
- JEE Main - 2025
- Mathematics
- Trigonometry
- If \[ \sum_{r=1}^{13} \frac{1}{\sin \frac{\pi}{4} + (r-1) \frac{\pi}{6}} \sin \frac{\pi}{4} + \frac{\pi}{6} = a \sqrt{3} + b, \quad a, b \in \mathbb{Z}, { then } a^2 + b^2 { is equal to:} \]
- JEE Main - 2025
- Mathematics
- Trigonometry
- The value of \( \cos \left( \frac{\pi}{6} + \cot^{-1}(-\sqrt{3}) \right) \) is:
- CBSE CLASS XII - 2025
- Mathematics
- Trigonometry
Questions Asked in KEAM exam
- In the measurement of length 6 $\mu$m is equal to $x$ pm. Then the value of $x$ is
- KEAM - 2024
- Dimensional Analysis
- If the lines \( \frac{x-1}{2} = \frac{y-2}{\alpha} = \frac{z-3}{2} \) and \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{-2} \) are perpendicular, then the value of \( \alpha \) is:
- KEAM - 2024
- Integration
- An organic compound contains 37.5% C, 12.5% H and the rest oxygen. What is the empirical formula of the compound?
- KEAM - 2024
- Oxygen
- Let A, B, C denote the set of students in a college who play football, basketball, and cricket respectively. If \( n(A) = 60 \), \( n(B) = 55 \), \( n(C) = 70 \), \( n(A \cup B \cup C) = 100 \) and \( n(A \cap B \cap C) = 20 \), then the number of students who play exactly two of these sports is
- KEAM - 2024
- Relations and functions
For the reaction:
\[ 2A + B \rightarrow 2C + D \]
The following kinetic data were obtained for three different experiments performed at the same temperature:
\[ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline I & 0.10 & 0.10 & 0.10 \\ II & 0.20 & 0.10 & 0.40 \\ III & 0.20 & 0.20 & 0.40 \\ \hline \end{array} \]
The total order and order in [B] for the reaction are respectively:
- KEAM - 2024
- Grignard’s reagents and their uses
Concepts Used:
Some Applications of Trigonometry
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It has many practical applications in various fields, including science, engineering, architecture, and navigation. Here are some examples:
- Architecture: Trigonometry is used in designing buildings and structures, particularly in determining the height and angles of roofs, the dimensions of rooms, and the placement of windows.
- Engineering: Trigonometry is used in many engineering fields, such as civil, mechanical, and electrical engineering. It is used to calculate the angles, distances, and dimensions of objects in 2D and 3D space, as well as to solve complex problems involving force, motion, and energy.
- Astronomy: Trigonometry is used to calculate the positions and movements of celestial bodies, such as planets and stars.
- Surveying: Trigonometry is used in surveying to measure distances, heights, and angles of land features, as well as to create maps and blueprints.
- Navigation: Trigonometry is used in navigation, both on land and at sea, to determine position, distance, and direction. It is also used in aviation to calculate the trajectory and speed of airplanes.
- Physics: Trigonometry is used in physics to calculate the behavior of waves, such as sound and light waves, and to solve problems involving motion and force.
Read Also: Some Applications of Trigonometry
Overall, trigonometry is a versatile tool that has many practical applications in various fields and continues to be an essential part of modern mathematics.