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
Correct Answer: B
Solution :
\[\tan (x+y)+\tan (x-y)=1\] Differentiating w.r.t. x of y, we get Þ \[{{\sec }^{2}}(x+y)\left( 1+\frac{dy}{dx} \right)+{{\sec }^{2}}(x-y)\left( 1-\frac{dy}{dx} \right)=0\] Þ \[\frac{dy}{dx}=\frac{{{\sec }^{2}}(x+y)+{{\sec }^{2}}(x-y)}{{{\sec }^{2}}(x-y)-{{\sec }^{2}}(x+y)}\].
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