Mister Exam
(sin2t)-((sin(t)+cos(t))^2)/(tg(t)+ctg(t)) inequation
The solution
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2
(sin(t) + cos(t))
sin(2*t) - ------------------ > 0
tan(t) + cot(t)
$$- \frac{\left(\sin{\left(t \right)} + \cos{\left(t \right)}\right)^{2}}{\tan{\left(t \right)} + \cot{\left(t \right)}} + \sin{\left(2 t \right)} > 0$$
-(sin(t) + cos(t))^2/(tan(t) + cot(t)) + sin(2*t) > 0
Rapid solution 2
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pi pi pi
(0, --) U (--, --)
4 4 2
$$x\ in\ \left(0, \frac{\pi}{4}\right) \cup \left(\frac{\pi}{4}, \frac{\pi}{2}\right)$$
x in Union(Interval.open(0, pi/4), Interval.open(pi/4, pi/2))
Rapid solution
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/ / pi\ /pi pi\\ Or|And|0 < t, t < --|, And|-- < t, t < --|| \ \ 4 / \4 2 //
$$\left(0 < t \wedge t < \frac{\pi}{4}\right) \vee \left(\frac{\pi}{4} < t \wedge t < \frac{\pi}{2}\right)$$
((0 < t)∧(t < pi/4))∨((pi/4 < t)∧(t < pi/2))