Let \[\Delta =\] \[\left| \begin{matrix} \sin x & \sin (x+h) & \sin (x+2h) \\ \sin (x+2h) & \sin x & \sin (x+h) \\ \sin (x+h) & \sin (x+2h) & \sin x \\ \end{matrix} \right|\]Then, \[\underset{h\to 0}{\mathop{\lim }}\,\,\,\left( \frac{\Delta }{{{h}^{2}}} \right)\] is

Let \[\Delta =\] \[\left| \begin{matrix} \sin x & \sin (x+h) & \s

1.	Let \[\Delta =\] \[\left\| \begin{matrix} \sin x & \sin (x+h) & \sin (x+2h) \\ \sin (x+2h) & \sin x & \sin (x+h) \\ \sin (x+h) & \sin (x+2h) & \sin x \\ \end{matrix} \right\|\]Then, \[\underset{h\to 0}{\mathop{\lim }}\,\,\,\left( \frac{\Delta }{{{h}^{2}}} \right)\] is
A.	\[9si{{n}^{2}}x\cos x\]
B.	\[3{{\cos }^{2}}x\]
C.	\[\sin x{{\cos }^{2}}x\]
D.	None of these
Answer» C. \[\sin x{{\cos }^{2}}x\]

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Let \[\Delta =\] \[\left| \begin{matrix} \sin x & \sin (x+h) & \sin (x+2h) \\ \sin (x+2h) & \sin x & \sin (x+h) \\ \sin (x+h) & \sin (x+2h) & \sin x \\ \end{matrix} \right|\]Then, \[\underset{h\to 0}{\mathop{\lim }}\,\,\,\left( \frac{\Delta }{{{h}^{2}}} \right)\] is

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