Question:medium

If \(\cos \alpha + \cos \beta + \cos \gamma = \sin \alpha + \sin \beta + \sin \gamma = 0\) then the value of \(\cos 3\alpha + \cos 3\beta + \cos 3\gamma\) is

Show Hint

Use complex numbers: \(z_1+z_2+z_3=0 \Rightarrow z_1^3+z_2^3+z_3^3=3z_1z_2z_3\).

Updated On: Apr 23, 2026

\(3\cos(\alpha+\beta+\gamma)\)
\(3\sin(\alpha+\beta+\gamma)\)
\(3\cos(\alpha+\beta+\gamma)\)
0

Show Solution

The Correct Option is C

Solution and Explanation

Was this answer helpful?

0

Top Questions on Series

If \( \sum_{k=1}^{n} k(k+1)(k-1) = pn^4 + qn^3 + tn^2 + sn \), where \( p, q, t, s \) are constants, then the value of \( s \) is equal to:
- BITSAT - 2024
- Mathematics
- Series
View Solution
There are four numbers of which the first three are in GP and the last three are in AP, whose common difference is 6. If the first and the last numbers are equal, then the two other numbers are:
- BITSAT - 2024
- Mathematics
- Series
View Solution
If \( A = 1 + r^a + r^{2a} + r^{3a} + \dots \infty \) and \( B = 1 + r^b + r^{2b} + r^{3b} + \dots \infty \), then \( \frac{a}{b} \) is equal.
- BITSAT - 2024
- Mathematics
- Series
View Solution
The sum of the infinite series \(1 + \frac{5}{6} + \frac{12}{6^2} + \frac{22}{6^3} + \frac{35}{6^4} + \dots\) is equal to:
- BITSAT - 2024
- Mathematics
- Series
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in MET exam

At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as

MET - 2018
Electrostatics

A charged particle travels along a straight line with a speed $\nu$ in a region where both electric field $\mathbf{E}$ and magnetic fields $\mathbf{B}$ are present. It follows that}

MET - 2018
Magnetic Effects of Current and Magnetism

A solenoid of length $50~\mathrm{cm}$ and a radius of cross-section $1\mathrm{cm}$ has 1000 turns of wire wound over it. If the current carried is 5A, the magnetic field on its axis, near the centre of the solenoid is approximately (permeability of free space $\mu_{0} = 4\pi \times 10^{-7}\mathrm{T}\cdot \mathrm{m / A}$)

MET - 2018
Magnetic Effects of Current and Magnetism

A transformer of $100%$ efficiency has 200 turns in the primary and 40000 turns in secondary. It is connected to a $220~\mathrm{V}$ main supply and secondary feeds to a $100\mathrm{k}\Omega$ resistance. The potential difference per turn is

MET - 2018
Electromagnetic induction