化简:(1)1/2cosx-√3/2sinx(2)√3sinx+cosx(3)√2(sinx-cosx)(4)√2cos
1个回答

(1)1/2cosx-√3/2sinx

=sinπ/6 cosx-cosπ/6 sinx

=sin(π/6-x)

(2)√3sinx+cosx

=2(√3/2sinx+1/2 cosx)

=2(cosπ/6sinx+sinπ/6cosx)

=2sin(x+π/6)

(3)√2(sinx-cosx)

=2(√2/2sinx-√2/2cosx)

=2(cosπ/4 sinx-sinπ/4 cosx)

=2sin(x-π/4)

(4)√2cosx-√6sinx

=2√2(1/2 cosx-√3/2 sinx)

=2√2(sinπ/6 cosx-cosπ/6 sinx)

=2√2 sin(π/6-x)

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