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

Solve : y = sin x + cos x

Prove that (cos x- cos y ) ^2 + ( sin x - sin y ) ^2 = 4 sin ^2"" ((x-y))/(2)

(cos x + cos y ) ^(2) + (sin x - sin y ) ^(2) = 4 cos ^(2) ""(x + y )/( 2)

(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)

Show that ( sin x + sin y) /( cos x + cos y) = tan ""(x+y)/(2)

Let x, y, in R satisfy the condition such that sin x sin y + 3 cos y +4 sin y cos x=sqrt(26) . The value of tan^(2)x + cot^(2)y is equal to

Solve the differential equation (x dy - y dx) y sin ((y)/(x)) = (y dx + x dy) x cos ((y)/(x)) .

y = e^(x)(a cos x + b sin x)

{ xcos ((y)/(x)) + y sin ((y)/(x))} y dx = { y sin ((y)/(x)) - x cos ((y)/(x))}x dy