Question:medium
The value of $\begin{vmatrix} \sin 30^{\circ} & \cos 30^{\circ} & \sin(30^{\circ}+75^{\circ}) \\ \sin 45^{\circ} & \cos 45^{\circ} & \sin(45^{\circ}+75^{\circ}) \\ \sin 60^{\circ} & \cos 60^{\circ} & \sin(60^{\circ}+75^{\circ}) \end{vmatrix}$ is equal to
The value of $\begin{vmatrix} \sin 30^{\circ} & \cos 30^{\circ} & \sin(30^{\circ}+75^{\circ}) \\ \sin 45^{\circ} & \cos 45^{\circ} & \sin(45^{\circ}+75^{\circ}) \\ \sin 60^{\circ} & \cos 60^{\circ} & \sin(60^{\circ}+75^{\circ}) \end{vmatrix}$ is equal to
Show Hint
Logic Tip: In matrix problems involving trigonometric sum or difference formulas across rows or columns, look for linear dependence immediately rather than calculating and evaluating each sine/cosine value individually.
Updated On: Apr 27, 2026
- -2
- -1
- 0
- 1
- 2
Show Solution
The Correct Option is C
Solution and Explanation
Was this answer helpful?
0
Top Questions on Determinants
- If \( f(x) \) is differentiable at \( x = 1 \) and \[ \lim_{h \to 0} \frac{1}{h} f(1 + h) = 5, \] then \( f'(1) \) is equal to:
- MHT CET - 2024
- Mathematics
- Determinants
- If \( A = \begin{bmatrix} 2 & 1
3 & 4 \end{bmatrix} \), then the determinant of matrix \( A \) is:- MHT CET - 2025
- Mathematics
- Determinants
- Evaluate the determinant of the matrix: \[ \left| \begin{array}{cc} 1 & \tan x
-\tan x & 1 \end{array} \right| \]- MHT CET - 2025
- Mathematics
- Determinants
- Find the value of the determinant \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \).
- MHT CET - 2025
- Mathematics
- Determinants
- Want to practice more? Try solving extra ecology questions todayView All Questions
