求值cos5π⼀8cosπ⼀8

解cos5π/8cosπ/8,请写出过程。 谢谢。
2024-12-17 03:22:30
推荐回答(2个)
回答1:

cos(5π/8+π/8)=cos5π/8cosπ/8-sin5π/8sinπ/8=-√2/2
cos(5π/8-π/8)=cos5π/8cosπ/8+sin5π/8sinπ/8=0

两式相加2cos5π/8cosπ/8=-√2/2
cos5π/8cosπ/8=-√2/4

回答2:

cos5π/8cosπ/8
=[cos(5π/8+π/8)+cos(5π/8-π/8)]/2
=(cos3π/4+cosπ/2)/2
=(cos3π/4)/2
=-√2/4