2*atan(sin(x))*cos(x)
---------------------
2
1 + sin (x)
$$\frac{2 \cos{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} + 1}$$
/ 2 2 \
| cos (x) 2*cos (x)*atan(sin(x))*sin(x)|
2*|----------- - atan(sin(x))*sin(x) - -----------------------------|
| 2 2 |
\1 + sin (x) 1 + sin (x) /
---------------------------------------------------------------------
2
1 + sin (x)
$$\frac{2 \left(- \sin{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)} - \frac{2 \sin{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} + 1} + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}\right)}{\sin^{2}{\left(x \right)} + 1}$$
/ 2 2 2 2 2 \
| 3*sin(x) 6*cos (x)*sin(x) 2*cos (x)*atan(sin(x)) 6*sin (x)*atan(sin(x)) 8*cos (x)*sin (x)*atan(sin(x))|
2*|-atan(sin(x)) - ----------- - ---------------- - ---------------------- + ---------------------- + ------------------------------|*cos(x)
| 2 2 2 2 2 |
| 1 + sin (x) / 2 \ 1 + sin (x) 1 + sin (x) / 2 \ |
\ \1 + sin (x)/ \1 + sin (x)/ /
--------------------------------------------------------------------------------------------------------------------------------------------
2
1 + sin (x)
$$\frac{2 \left(- \operatorname{atan}{\left(\sin{\left(x \right)} \right)} + \frac{6 \sin^{2}{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} + 1} - \frac{3 \sin{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} - \frac{2 \cos^{2}{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} + 1} + \frac{8 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\left(\sin^{2}{\left(x \right)} + 1\right)^{2}} - \frac{6 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\sin^{2}{\left(x \right)} + 1\right)^{2}}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}$$