Math Problem Solver

\[15 {\sin\left( -74.5 \right)}^{2} - 26 \cdot \cos\left( -74.5 \right) - 23 = -23 - 26 \cos{\left(\frac{149}{2} \right)} + 15 \sin^{2}{\left(\frac{149}{2} \right)} \approx -30.01995382762100168931672394730318\]

\[\begin{aligned}15 {\sin\left( -74.5 \right)}^{2} - 26 \cdot \cos\left( -74.5 \right) - 23& = 15 \cdot \sin^{2}{\left(- \left(74 + \frac{5}{10}\right) \right)} - 26 \cdot \cos{\left(- \left(74 + \frac{5}{10}\right) \right)} - 23\\& = 15 \cdot \sin^{2}{\left(- \left(74 + \frac{1}{2}\right) \right)} - 26 \cdot \cos{\left(- \left(74 + \frac{5}{10}\right) \right)} - 23\\& = 15 \cdot \sin^{2}{\left(- \frac{149}{2} \right)} - 26 \cdot \cos{\left(- \left(74 + \frac{5}{10}\right) \right)} - 23\\& = 15 \cdot \left(- \sin{\left(\frac{149}{2} \right)}\right)^{2} - 26 \cdot \cos{\left(- \left(74 + \frac{5}{10}\right) \right)} - 23\\& = 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)} - 26 \cdot \cos{\left(- \left(74 + \frac{5}{10}\right) \right)} - 23\\& = 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)} - 26 \cdot \cos{\left(- \left(74 + \frac{1}{2}\right) \right)} - 23\\& = 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)} - 26 \cdot \cos{\left(- \frac{149}{2} \right)} - 23\\& = 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)} - 26 \cdot \cos{\left(\frac{149}{2} \right)} - 23\\& = \left(-26 \cdot \cos{\left(\frac{149}{2} \right)} + 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)}\right) - 23\\& = -23 - 26 \cdot \cos{\left(\frac{149}{2} \right)} + 15 \cdot \sin^{2}{\left(\frac{149}{2} \right)}\end{aligned}\]