1.

 If \[\tan (x+y)+\tan (x-y)=1,\]then \[\frac{dy}{dx}=\] [DSSE 1979]

A.            \[\frac{{{\sec }^{2}}(x+y)+{{\sec }^{2}}(x-y)}{{{\sec }^{2}}(x+y)-{{\sec }^{2}}(x-y)}\]
B.            \[\frac{{{\sec }^{2}}(x+y)+{{\sec }^{2}}(x-y)}{{{\sec }^{2}}(x-y)-{{\sec }^{2}}(x+y)}\]
C.            \[\frac{{{\sec }^{2}}(x+y)-{{\sec }^{2}}(x-y)}{{{\sec }^{2}}(x+y)+{{\sec }^{2}}(x-y)}\]
D.            None of these
Answer» C.            \[\frac{{{\sec }^{2}}(x+y)-{{\sec }^{2}}(x-y)}{{{\sec }^{2}}(x+y)+{{\sec }^{2}}(x-y)}\]


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