Solve the equation on the interval \( 0 \leq \theta<2 \pi \) \( (\cot \theta-1)(\csc \theta-1)=0 \)

Find an equation for a sinusoidal function that has period \( 3 \pi \), amplitude 3 , and contains the point \( \left(-\frac{3 \pi}{2}, 0\right) \)

Find an equation for a sinusoidal function that has period \( \pi \), amplitude \( \frac{1}{2} \), and contains the point \( \left(\frac{\pi}{2}, 0\right) \).

Дан треугольник \( A B C \), в котором \( \angle C=90^{\circ} \), а \( \sin B=\frac{4 \sqrt{3}}{10} \). Найд \( \cos ^{2} B \).

Find an equation for a sinusoidal function that has period \( 2 \pi \), amplitude 1 , and contains the point \( \left(-\frac{\pi}{2}, 3\right) \)

Дан треугольник \( A B C \), в котором \( \angle A+\angle B=90^{\circ} \), а \( \sin B=\frac{2 \sqrt{5}}{10 \sqrt{10}} \) Найди \( \cos ^{2} B \).