Math Problem Solver

\[\frac{-3}{2 \cdot \sin\left( \frac{49 \cdot \pi}{20} \right)} + 1 = 1 - \frac{3}{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \sqrt{2} \cdot \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)} \approx -0.51869768868200439704261597448187\]

\[\begin{aligned}\frac{-3}{2 \cdot \sin\left( \frac{49 \cdot \pi}{20} \right)} + 1& = -3 \cdot \frac{1}{2 \cdot \sin{\left(49 \cdot \frac{\pi}{20} \right)}} + 1\\& = -3 \cdot \frac{1}{2 \cdot \sin{\left(\frac{49}{20} \cdot \pi \right)}} + 1\\& = -3 \cdot \frac{1}{2 \cdot \left(\frac{1}{2} \cdot \sqrt{2} \cdot \sqrt{\frac{5}{8} - \frac{1}{8} \cdot \sqrt{5}} + \frac{1}{2} \cdot \sqrt{2} \cdot \left(\frac{1}{4} + \frac{1}{4} \cdot \sqrt{5}\right)\right)} + 1\\& = -3 \cdot \frac{1}{\sqrt{2} \cdot \sqrt{\frac{5}{8} - \frac{1}{8} \cdot \sqrt{5}} + \sqrt{2} \cdot \left(\frac{1}{4} + \frac{1}{4} \cdot \sqrt{5}\right)} + 1\\& = 1 - 3 \cdot \frac{1}{\sqrt{2} \cdot \sqrt{\frac{5}{8} - \frac{1}{8} \cdot \sqrt{5}} + \sqrt{2} \cdot \left(\frac{1}{4} + \frac{1}{4} \cdot \sqrt{5}\right)}\end{aligned}\]