Question

Find the equation of the tangents to the curve, y = cos(x+y), -2≤ x≤ 2Π, that are parallel to the line x + 2y = 0.

Answer 1

$given \: \: \: y = \cos(x + y) \\ \frac{dy}{dx} = - \sin(x + y) (1 + \frac{dy}{dx} ) \\ \frac{dy}{dx} = \frac{ - \sin(x + y) }{1 + \sin(x + y) } \\ tangent \: is \: parallel \: to \: x + 2y = 0 \\ slope \: of \: tangent = \frac{ - 1}{2} \\ \frac{ - 1}{2} = \frac{ - \sin(x + y) }{1 + \sin(x + y) } \\ \sin(x + y ) = 1 \\ x + y = 90 \\ so \: x + y \: = 90 \: is \: our \: required \\ tangent \: equation$
plz tell me if it is wrong