Determinants Matrices Question 60
Question: If $ y= \begin{vmatrix} \sin x & \cos x & \sin x \\ \cos x & -sinx & \cos x \\ x & 1 & 1 \\ \end{vmatrix}, $ then $ \frac{dy}{dx} $ is
Options:
A) $ 1 $
B) $ 2 $
C) $ 3 $
D) 0
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ \frac{dy}{dx}= \begin{vmatrix} \cos x & -\sin x & \cos x \\ \cos x & -\sin x & \cos x \\ x & - & - \\ \end{vmatrix} $
$ + \begin{vmatrix} \sin x & \cos x & sinx \\ -\sin x & -\cos x & -\sin x \\ x & 1 & 1 \\ \end{vmatrix} $
$ + \begin{vmatrix} \sin x & \cos x & sinx \\ \cos x & -sinx & \cos x \\ x & 0 & 0 \\ \end{vmatrix} $
$ =0- \begin{vmatrix} \sin x & \cos x & sinx \\ sinx & \cos x & sinx \\ x & 1 & 1 \\ \end{vmatrix} $
$ +1 \begin{vmatrix} \cos x & \sin x \\ -\sin x & \cos x \\ \end{vmatrix} $
$ =0+({{\cos }^{2}}x+{{\sin }^{2}}x) $
BETA
