cos(x+y)=y sin x

Prove that |(1,x,y),(0, sin x, sin y),(0, cos x,cos y)|= sin (x-y)

{x cos (y/x)+y sin (y/x)} y d x={y sin (y/x)-(x) cos (y/x)} x d y

Solve the following differential equations y{x cos (y/x)+y sin (y/x)}dx- x{ y sin (y/x)-x cos (y/x)}dy=0 .

y-cos y=x:(y sin y+cos y+x)y'=y .

cos (x + y), sin (x + y), - cos (x + y) sin (xy), cos (xy), sin (xy) sin2x, 0, sin2y] | = sin2 (x + y)

The area of the region bounded by the curve y= cos x,y = sin x,Y -axis and 0 le x le (pi)/(4) is ……. Sq. units.

|{:(cos(x+y),sin(x+y),-cos(x+y)),(sin(x-y),cos(x-y),sin(x-y)),(sin2x,0,sin2y):}|=sin2(x+y)