Question

Solution of the differential equation $ \tan y.{{\sec }^{2}}xdx+\tan x.{{\sec }^{2}}ydy=0 $ is:

• 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

Answer 1

Answer: (D)

$ \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 $