Answer:
Use Trigonometric formulae to simplify expressions
Step-by-step explanation:
Re-order to group the x and y,
Sin(y) / Sin(a+y) = x
to differentiate apply d/dx to both sides
[tex]\frac{d}{dx}[/tex]Sin(y) / Sin(a+y) = [tex]\frac{d}{dx}[/tex]x
use division rule on left side which will give
[tex]\frac{dy}{dx}[/tex]Cos(y)Sin(a+y) - [tex]\frac{dy}{dx}[/tex]Cos(a+y)Sin(y) / Sin²(a+y) = 1
Group them so dy/dx is on the left hand side:
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)Sin(a+y) - Cos(a+y)Sin(y)
Apply trigonometric sum formula to expand Sin(a+y) and Cos(a+y),
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)[Sin(a)Cos(y) + Cos(a)Sin(y)] - Sin(y)[Cos(a)Cos(y) - Sin(a)Sin(y)]
Simplify it
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (Cos²(y) + Sin²(y))(Sin(a))
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (1)(Sin(a))
