f(x)=sin(4分之派－x)分之cos2x化简

急

2025-06-29 00:51:00

推荐回答（3个）

回答1：

f(x)=sin(4分之派－x)分之cos2x
=(cos^2x-sin^2x)/(根号2/2cosx-根号2/2sinx)
=(cosx+sinx)(cosx-sinx)/[(根号2/2)*(cosx-sinx)]
=根号2(cosx+sinx)
=2sin(x+Pai/4)

回答2：

f(x) = cos2x / sin(π/4-x)
= (cos^2x-sin^2x) / (sinπ/4cosx-cosπ/4sinx)
= (cosx+sinx) / (cosx-sinx) / [√2/2(cosx-sinx)]
= √2(sinx+cosx)
= 2(sinxcosπ/4+cosxsinπ/4)
= 2sin(x+π/4)

定义域sin(π/4-x)≠0，x≠kπ+π/4

回答3：

2sin(x+π/4)