Question

已知f（x）=sinx+cosx，则f（π/12）=？请写过程，谢谢

Answer 1

答：f（x）=sinx+cosx
=sinx+sin(π/2-x)
=2sin(x+π/2-x)/2cos(x-π/2+x)/2
=2sinπ/4cos(x-π/4)
=√2cos（x-π/4)
所以，f(π/12) = √2cos（π/12-π/4) =√2cos（π/6)
=√6/2

Answer 2

f(x) = √2[(sinx)(√2/2) + (cosx)(√2/2)]
= √2[sinxcos(π/4) + cosxsin(π/4)]
= √2sin(x + π/4)
f(π/12) = √2sin(π/12 + π/4) = √2sin(π/3)
= √2*√3/2
= √6/2