化简:(cos(π/4+a)-sin(π/4+a))/(cos(π/4-a)+sin(π/4-a))
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化简:(cos(π/4+a)-sin(π/4+a))/(cos(π/4-a)+sin(π/4-a))
(cos(π/4+a)-sin(π/4+a))/(cos(π/4-a)+sin(π/4-a))
分子分母同乘以根号2/2:
(sinπ/4 cos(π/4+a)-cosπ/4 sin(π/4+a))/(cosπ/4 cos(π/4-a)+sinπ/4 sin(π/4-a))
= sin(π/4 - π/4 - a) / cos(π/4-π/4+a)
= sin(-a) / cosa
= - sina / cosa
= -tan a
分子分母同乘以根号2/2:
(sinπ/4 cos(π/4+a)-cosπ/4 sin(π/4+a))/(cosπ/4 cos(π/4-a)+sinπ/4 sin(π/4-a))
= sin(π/4 - π/4 - a) / cos(π/4-π/4+a)
= sin(-a) / cosa
= - sina / cosa
= -tan a
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