Question:
If \(\frac {3cos\ 2x+cos^32x}{cos^6x-sin^6x}=x^3-x^2+6\), then find sum of roots.
If \(\frac {3cos\ 2x+cos^32x}{cos^6x-sin^6x}=x^3-x^2+6\), then find sum of roots.
Updated On: Mar 20, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 1
Solution and Explanation
The answer is 1.
Was this answer helpful?
0
0
Top Questions on Some Applications of Trigonometry
- A ladder 7 m long makes an angle of 30\(^\circ\) with the wall. Find the height of the point on the wall where the ladder touches the wall.
- Bihar Board X - 2025
- Mathematics
- Some Applications of Trigonometry
- The angle of elevation of the top of a tower at a distance of 10 m from its base is 60\(^\circ\); then the height of the tower is
- Bihar Board X - 2025
- Mathematics
- Some Applications of Trigonometry
- A kite is at a height of 30 m from the earth and its string makes an angle 60\(^\circ\) with the earth. Then the length of the string is
- Bihar Board X - 2025
- Mathematics
- Some Applications of Trigonometry
- The shadow of a tower, when the angle of elevation of the sun is $30^\circ$, is $50$ m longer than when the angle of elevation was $60^\circ$ on the plane ground. Find the height of the tower.
- UP Board X - 2025
- Mathematics
- Some Applications of Trigonometry
- Let $$ \alpha = \frac{1}{\sin 60^\circ \sin 61^\circ} + \frac{1}{\sin 62^\circ \sin 63^\circ} + \cdots + \frac{1}{\sin 118^\circ \sin 119^\circ}. $$ Then the value of $$ \left( \frac{\csc 1^\circ}{\alpha} \right)^2 $$ is \rule{1cm}{0.15mm}.
- JEE Advanced - 2025
- Mathematics
- Some Applications of Trigonometry
View More Questions
Questions Asked in JEE Main exam
A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field \( B \) exists into the page. The bar starts to move from the vertex at time \( t = 0 \) with a constant velocity. If the induced EMF is \( E \propto t^n \), then the value of \( n \) is _____.
- JEE Main - 2025
- Magnetic Field
- Concentrated nitric acid is labelled as 75%by mass. The volume in mL of the solution which contains 30 g of nitric acid is: Given: Density of nitric acid solution is 1.25 g/mL.
- JEE Main - 2025
- Solutions
- A physical quantity \( Q \) is related to four observables \( a \), \( b \), \( c \), and \( d \) as follows: \[ Q = \frac{a b^4}{c d^2} \] Where:
- \( a = (60 \pm 3) \, \text{Pa} \),
- \( b = (20 \pm 0.1) \, \text{m} \),
- \( c = (40 \pm 0.2) \, \text{N·s/m}^2 \),
- \( d = (50 \pm 0.1) \, \text{m} \).
Then the percentage error in \( Q \) is:- JEE Main - 2025
- Error analysis
- Let circle $C$ be the image of
$$ x^2 + y^2 - 2x + 4y - 4 = 0 $$
in the line
$$ 2x - 3y + 5 = 0 $$
and $A$ be the point on $C$ such that $OA$ is parallel to the x-axis and $A$ lies on the right-hand side of the centre $O$ of $C$.
If $B(\alpha, \beta)$, with $\beta < 4$, lies on $C$ such that the length of the arc $AB$ is $\frac{1}{6}$ of the perimeter of $C$, then $\beta - \sqrt{3}\alpha$ is equal to: - Assume a living cell with 0.9%(\(w/w\)) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data up to first decimal place only) The cell will:
- JEE Main - 2025
- osmosis
View More Questions
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.