请问为什么√2*sin(πx/8+π/4)+√2*cos(xπ/8+π/4)=2cos(πx/8).
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请问为什么√2*sin(πx/8+π/4)+√2*cos(xπ/8+π/4)=2cos(πx/8).
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因为cos(a-b)=cosacosb+sinasinb
cosπ/4=sinπ/4=√2 / 2
原式=2[(√2 / 2) sin(πx/8+π/4)+(√2 / 2)*cos(xπ/8+π/4)]
=2[sinπ/4 * sin(πx/8+π/4)+ cosπ/4 *cos(xπ/8+π/4)]
=2cos(πx/8)
cosπ/4=sinπ/4=√2 / 2
原式=2[(√2 / 2) sin(πx/8+π/4)+(√2 / 2)*cos(xπ/8+π/4)]
=2[sinπ/4 * sin(πx/8+π/4)+ cosπ/4 *cos(xπ/8+π/4)]
=2cos(πx/8)
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