Answer to Question #225116 in Trigonometry for Amit

Question #225116

Problem C

Determine the numerical value of the following expression without the use of a calculator: 

problem is found on the website below


https://docs.google.com/viewerng/viewer?url=https://iymc.info/docs/IYMC_Qualification_Round_2021.pdf


1
Expert's answer
2021-08-23T07:30:20-0400

"\\sqrt{\\sin\\left(\\frac{\\pi+\\log_2(\\sqrt{2^\\pi\\cdot2^\\pi})}{2^5-2^4-2^3}\\right)\\cdot\\sqrt[3]{\\frac{2^{4-1}}{2^{3\/2}}}+\\log_2(\\log_3(9^{15})+\\pi^{1+(-1)^{17}}+1)+\\frac{(-1)^5+(-1)^{27}}{(-1)^{766}}}=\\\\\n{}=\\sqrt{\\sin\\left(\\frac{\\pi+\\log_2(\\sqrt{2^{2\\pi}})}{32-16-8}\\right)\\cdot\\sqrt[3]{\\frac{2^{3}}{2^{3\/2}}}+\\log_2(\\log_3(3^{30})+\\pi^{1-1}+1)+\\frac{-1-1}{1}}=\\\\\n{}=\\sqrt{\\sin\\left(\\frac{\\pi+\\log_2(2^{\\pi})}{8}\\right)\\cdot\\sqrt[3]{2^{3\/2}}+\\log_2(30+1+1)-2}=\\\\\n{}=\\sqrt{\\sin\\left(\\frac{\\pi+\\pi}{8}\\right)\\cdot\\sqrt{2}+\\log_2(32)-2}=\\sqrt{\\sin\\left(\\frac{\\pi}{4}\\right)\\cdot\\sqrt{2}+\\log_2(2^5)-2}=\\\\\n{}=\\sqrt{\\frac{\\sqrt2}2\\cdot\\sqrt{2}+5-2}=\\sqrt{1+3}=\\sqrt4=2."



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