calculus invers function

[newton333]

[Crimson Sunbird]

[latex]\sin x+\sin y = 2\sin\frac{x+y}2\cos\frac{x-y}2=\pm2\sin\frac{x+y}2\sqrt{1-\sin^2\frac{x-y}2}[/latex]

NB: [latex]\cos\frac{x-y}2=\color{red}\pm\color{black}\sqrt{1-\sin^2\frac{x-y}2}[/latex] as [latex]\cos\frac{x-y}2[/latex] can be negative (e.g. when [latex]x=270^{\circ},y=30^{\circ}[/latex]).

[newton333]

thank you