Addition Formulas

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sin$\left(\vphantom{ x+y}\right.$x + y$\left.\vphantom{ x+y}\right)$ =  sin x cos y + cos x sin y

cos$\left(\vphantom{ x+y}\right.$x + y$\left.\vphantom{ x+y}\right)$ =  cos x cos y - sin x sin y

tan$\left(\vphantom{ x+y}\right.$x + y$\left.\vphantom{ x+y}\right)$ =  ${\dfrac{{\sin x\cos y+\cos x\sin y}}{{\cos x\cos y-\sin x\sin y}}}$

Apply Combine + Trig Functions to the expansions of sin$\left(\vphantom{ x+y}\right.$x + y$\left.\vphantom{ x+y}\right)$ and cos$\left(\vphantom{ x+y}\right.$x + y$\left.\vphantom{ x+y}\right)$ to return them to their original form and to change the expansion of tan$\left(\vphantom{ x+y}\right.$x + y$\left.\vphantom{ x+y}\right)$ to the form  ${\frac{{\sin \left( x+y\right) }}{{\cos \left( x+y\right) }}}$.