A) \[tan\text{ }x+tan\text{ }y=k\]
B) \[tan\text{ }x-tan\text{ }y=k\]
C) \[(tan\text{ }x/tan\text{ }y)=k\]
D) \[tan\text{ }x.tan\text{ }y=k\]
E) None of the above
Correct Answer: D
Solution :
\[\tan y{{\sec }^{2}}xdx+\tan x{{\sec }^{2}}ydy=0\] \[\Rightarrow \] \[\int{\frac{{{\sec }^{2}}x}{\tan x}}dx+\int{\frac{{{\sec }^{2}}y}{\tan y}}dy=0\] \[\Rightarrow \] \[\log \tan x+\log \tan y=\log k\] \[\Rightarrow \] \[\tan x\tan y=k\]
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