A) \[\sin 2u\]
B) \[\cos 2u\]
C) \[\tan 2u\]
D) \[\sec 2u\]
Correct Answer: A
Solution :
\[\tan u\] is homogeneous in x, y of degree 2. \[\therefore \] \[x\frac{\partial }{\partial x}(\tan u)+y\frac{\partial }{\partial y}(\tan u)=2(\tan u)\] \[\therefore \] \[x{{\sec }^{2}}u\frac{\partial u}{\partial x}+y{{\sec }^{2}}u\frac{\partial u}{\partial y}=2\tan u\] Þ \[x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=2\frac{\tan u}{{{\sec }^{2}}u}\] = \[2\sin u\cos u=\sin 2u\].
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