Question

已知函数f(x)={1-(√2)*sin[2x-(π/4)]}/cosx

Answer 1

(1)cosx≠0

x≠Kπ+π/2 K∈Z

(2)由tanα=-4/3可知:sinα=4/5,cosα=-3/5

得：sin2α=2sinα*cosα=-24/25

cos2α=1-2(sinα)^2=-7/25

f(α)=[1-√2sin(2α-π/4)]/cosα

=[1-√2(sin2α*cosπ/4-cos2α*sinπ/4)]/cosα

=[1-sin2α+cos2α]/cosα

=[1+24/25-7/25]/(-3/5)

=-14/5