Question

像2cosx-2sinx到底是应该化为2√2cos(π/4+x)还是化为2√2sin(π/4-x) 到底怎么看

Answer 1

2cosx-2sinx
= √2(√2/2cosx-√2/sinx)
= √2(cosxcosπ/4-sinxsinπ/4)
= √2cos(x+π/4)

2cosx-2sinx
= √2(√2/2cosx-√2/sinx)
= √2(cosxsinπ/4-sinxsinπ/4)
= √2sin(π/4-x)
= -√2sin(x-π/4)

两者是一样的。