Question

谁能告诉我这么你告诉我这是怎么算的啊 上大学都忘了…… sin(x)＋cos(...

谁能告诉我这么你告诉我这是怎么算的啊
上大学都忘了……
sin(x)＋cos(x)＝√2cos(π/4-x)

Answer 1

sin(x)＋cos(x)
=√2[(1/√2)sin(x)+(1/√2)cos(x)]
=√2[sin(π/4)sin(x)+cos(π/4)cos(x)]
＝√2cos(π/4-x)
(最后那一部是一个公式)

Answer 2

sinx＋cosx
=√2(sinx•√2/2＋cosx•√2/2)
=√2(sinx•cosπ/4＋cosx•sinπ/4)
=√2sin(x＋π/4)
=√2cos[π/2-(x＋π/4)] 诱导公式~!
=√2cos(π/4-x)