求值cos5π/8cosπ/8解cos5π/8cosπ/8,请写出过程.

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求值cos5π/8cosπ/8解cos5π/8cosπ/8,请写出过程.

求值cos5π/8cosπ/8解cos5π/8cosπ/8,请写出过程.
求值cos5π/8cosπ/8
解cos5π/8cosπ/8,请写出过程.

求值cos5π/8cosπ/8解cos5π/8cosπ/8,请写出过程.
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

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