If C = 2 cos q. Then value of the determinant D = (\left| \... | MATH - MINOR AND CO-FACTORS, PRODUCT OF DETERMINANTS | SolveeIt | Solveeit

Today, August 24

Question

If C = 2 cos q. Then value of the determinant

D = $\left| \begin{matrix} C & 1 & 0 \\ 1 & C & 1 \\ 6 & 1 & C \end{matrix} \right|$ is

A

$\frac{\sin 4\theta}{\sin\theta}$

B

$\frac{2\sin^{2}2\theta}{\sin\theta}$

C

4 cos²q(2 cosq –1)

D

None of these

Answer

None of these

Explanation

Solution

given that C = 2 – cos q

D = $\left| \begin{matrix} C & 1 & 0 \\ 1 & C & 1 \\ 6 & 1 & C \end{matrix} \right|$ = C(C² – 1) – 1(C – 6)

D = 2 cosq (4 cos²q – 1) – (2cosq – 6)

D = 4 cos³q – 4 cosq + 6