Question

(^ + 2 sin ) + ( ^ + ^2 cos ) = 0​

Answer 1

Answer:

Given sin2 x + 2 cos y + xy = 0

Differentiate both sides w.r.t.x

2 sin x cos x – 2 sin y(dy/dx) + (y + x dy/dx) = 0

(dy/dx)( x – 2 sin y) = (-y – 2 sin x cos x)

(dy/dx)( x – 2 sin y) = (-y – sin 2x)

(dy/dx) = (-y – sin 2x)/( x – 2 sin y)

= -(y + sin 2x)/( x – 2 sin y)

= (y + sin 2x)/( 2 sin y – x)