Question

X + sin(x + y) = y − cos (x − y)

Answer 1

Answer:

dxdy​=sin(x+y)+cos(x+y)

Put u=x+y⇒y=u−x⇒dxdy​=dxdu​−1

∴dxdu​−1=sinu+cosu⇒dxdu​=(1+cosu)+sinu

⇒dxdu​=2cos22u​+2sin2u​cos2u​

⇒21​sec22u​dxdu​=1+tan2u​

⇒21​⎝⎜⎛​tan2u​+1sec22u​​⎠⎟⎞​du=dx

Integrate on both sides

⇒log(1+tan2u​)=x+c

⇒log(1+tan2x+y​)=x+c

Step-by-step explanation: