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rotor63
@rotor63
October 2021
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30 баллов 4cos^2(π/8)-4cos^4(π/8)-4<br /> Нужны пояснения, плз. Ответ:-3.5
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DedushkaBake
Применим формулы 2cos²a-1=cos2a, a²-b²=(a-b)(a+b), cosπ/4=√2/2
=2(2cos²π/8-1)-4cos^4π/8-2=2cosπ/4-4cos^4+1-3=2(√2)/2-(4cos^4-1)-3=
√2-(2cos²π/8-1)(2cos²π/8+1)-3=√2-(√2/2)(2cos²π/8-1+2)-3
=√2-(√2/2)(cosπ/4+2)-3=√2-(√2/2)(√2/2+2)-3=√2-1/2-√2-3=-1/2-3=-3,5
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Answers & Comments
=2(2cos²π/8-1)-4cos^4π/8-2=2cosπ/4-4cos^4+1-3=2(√2)/2-(4cos^4-1)-3=
√2-(2cos²π/8-1)(2cos²π/8+1)-3=√2-(√2/2)(2cos²π/8-1+2)-3
=√2-(√2/2)(cosπ/4+2)-3=√2-(√2/2)(√2/2+2)-3=√2-1/2-√2-3=-1/2-3=-3,5