Question

simplify: (sin³a+cos³a/sin a+cos a) +sin a cos a

Answer 1

$$\begin{gathered} \frac{{\sin }^3\mathrm{a}+{\cos }^3\mathrm{a}}{\sin \mathrm{a}+\cos \mathrm{a}}+\sin \mathrm{a}.\cos \mathrm{a} \\ =\frac{\left(\sin \mathrm{a}+\cos \mathrm{a}\right)\left({\sin }^2\mathrm{a}+{\cos }^2\mathrm{a}-\sin \mathrm{a}.\cos \mathrm{a}\right)}{\left(\sin \mathrm{a}+\cos \mathrm{a}\right)}+\sin \mathrm{a}.\cos \mathrm{a} \\ =\left({\sin }^2\mathrm{a}+{\cos }^2\mathrm{a}-\sin \mathrm{a}.\cos \mathrm{a}\right)+\sin \mathrm{a}.\cos \mathrm{a} \\ =1-\sin \mathrm{a}.\cos \mathrm{a}+\sin \mathrm{a}.\cos \mathrm{a} \\ =1 \end{gathered}$$