Math Problem Solver

\[\frac{{\left( 1 + 1.53199 \cdot {\cos\left( 0.006873 \cdot 138.4884 + 6.225 \right)}^{2} \right)}^{\frac{3}{2}}}{\left\lvert 0.010529 \cdot -\sin\left( 0.006873 \cdot 138.4884 + 6.225 \right)\right\rvert} = \frac{1000000 \left(\frac{153199 \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}}{100000} + 1\right)^{\frac{3}{2}}}{10529 \sin{\left(\frac{17942076933}{2500000000} \right)}} \approx 246.97085671210108653890743062798175\]

\[\begin{aligned}\frac{{\left( 1 + 1.53199 \cdot {\cos\left( 0.006873 \cdot 138.4884 + 6.225 \right)}^{2} \right)}^{\frac{3}{2}}}{\left\lvert 0.010529 \cdot -\sin\left( 0.006873 \cdot 138.4884 + 6.225 \right)\right\rvert}& = \left(1 + \left(1 + \frac{53199}{100000}\right) \cdot \cos^{2}{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{1221}{2500}\right) + 6 + \frac{225}{1000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{6873}{1000000} \cdot \frac{346221}{2500} + 6 + \frac{225}{1000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{2379576933}{2500000000} + 6 + \frac{225}{1000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{2379576933}{2500000000} + 6 + \frac{9}{40} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17379576933}{2500000000} + \frac{9}{40} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{4884}{10000}\right) + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \left(138 + \frac{1221}{2500}\right) + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{6873}{1000000} \cdot \frac{346221}{2500} + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{2379576933}{2500000000} + 6 + \frac{225}{1000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{2379576933}{2500000000} + 6 + \frac{9}{40} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{17379576933}{2500000000} + \frac{9}{40} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{\frac{10529}{1000000} \cdot -1 \cdot \sin{\left(\frac{17942076933}{2500000000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\left|{- \frac{10529}{1000000} \cdot \sin{\left(\frac{17942076933}{2500000000} \right)}}\right|}\\& = \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\frac{10529}{1000000} \cdot \sin{\left(\frac{17942076933}{2500000000} \right)}}\\& = \frac{1000000}{10529} \cdot \left(1 + \frac{153199}{100000} \cdot \cos^{2}{\left(\frac{17942076933}{2500000000} \right)}\right)^{\frac{3}{2}} \cdot \frac{1}{\sin{\left(\frac{17942076933}{2500000000} \right)}}\end{aligned}\]