A) \[1\]
B) \[2\]
C) \[3\]
D) 0
Correct Answer: A
Solution :
[a] \[\frac{dy}{dx}=\left| \begin{matrix} \cos x & -\sin x & \cos x \\ \cos x & -\sin x & \cos x \\ x & - & - \\ \end{matrix} \right|\] \[+\left| \begin{matrix} \sin x & \cos x & sinx \\ -\sin x & -\cos x & -\sin x \\ x & 1 & 1 \\ \end{matrix} \right|\] \[+\left| \begin{matrix} \sin x & \cos x & sinx \\ \cos x & -sinx & \cos x \\ x & 0 & 0 \\ \end{matrix} \right|\] \[=0-\left| \begin{matrix} \sin x & \cos x & sinx \\ sinx & \cos x & sinx \\ x & 1 & 1 \\ \end{matrix} \right|\]\[+1\left| \begin{matrix} \cos x & \sin x \\ -\sin x & \cos x \\ \end{matrix} \right|\] \[=0+({{\cos }^{2}}x+{{\sin }^{2}}x)\]
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