Question

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

• A. $tanx+tany=k$
• B. $tanx-tany=k$
• C. $(tanx/tany)=k$
• D. $tanx.tany=k$
• E. None of the above

Answer 1

Answer: (D)

$\tan y{\sec }^{2}xdx+\tan x{\sec }^{2}ydy=0$ $\Rightarrow$ $\int \frac{{\sec }^{2}x}{\tan x}dx+\int \frac{{\sec }^{2}y}{\tan y}dy=0$ $\Rightarrow$ $\log \tan x+\log \tan y=\log k$ $\Rightarrow$ $\tan x\tan y=k$