题目
(cos π/8+ sin π/8 ) (cos^3 π/8+sin^3 π/8 )的值.
提问时间：2020-10-04
答案
(cos π/8+ sin π/8 ) (cos^3 π/8+sin^3 π/8 )
=[(cos π/8+ sin π/8 )^2] (cos^2 π/8-cosπ/8sinπ/8+sin^2 π/8 )
=(1+2cos π/8 sin π/8 ) (1-cosπ/8sinπ/8 )
=(1+sin π/4 ) [1-(1/2)sinπ/4]
=(1+√2/2) [1-(1/2)√2/2]
=(1+√2/2) (1-√2/4)
=(3+√2)/4
=[(cos π/8+ sin π/8 )^2] (cos^2 π/8-cosπ/8sinπ/8+sin^2 π/8 )
=(1+2cos π/8 sin π/8 ) (1-cosπ/8sinπ/8 )
=(1+sin π/4 ) [1-(1/2)sinπ/4]
=(1+√2/2) [1-(1/2)√2/2]
=(1+√2/2) (1-√2/4)
=(3+√2)/4
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