Question

slove the following dy/dx=cos(x+y)​

Answer 1

Answer:

tan((x+y)/ 2) =x

Step-by-step explanation:

dy/dx=cos(x+y) equn(1.)

z=x+y. equn(2.)

diff. w.r.t. x , we get,

dz/dx = 1 + dy/dx.

dz/dx = 1+ cos(x+y) from equn(1.)

dz/dx = 1+ cos z from equn(2.)

dz/(1+cosz) = dx.

dz/(2 cos^2(z/2)) = dx.

so, sec^2(z/2) dz / 2 =dx.

so, sec^2(z/2) dz = 2dx.

integarting both sides, we get

tan(z/2) / (1/2) = 2x.

so, 2tan(z/2) =2x.

so, tan(z/2) = x.

so, tan((x+y)/ 2) =x is ans