Question

已知函数f(x)=1-根号2sin(2x-π/4）/cosx

2）设a是第四象限的角，切tana=4/3求F（a)的值

Answer 1

f(x) = {1-√2sin(2x-π/4)}/cosx
= {1-(√2sin2xcosπ/4-cos2xsinπ/4)}/cosx
= {1-(sin2x-cos2x)}/cosx
= {1-sin2x+cos2x}/cosx
= {1-2sinxcosx+2cos^2x-1}/cosx
= {-2sinxcosx+2cos^2x}/cosx
= 2(cosx-sinx)
a是第四象限的角，切tana=4/3
sinx = -tanx/√(1+tan^2x) = -4/3 /√(1+16/9) = -4/5
cosx = 1/√(1+tan^2x) = 1 /√(1+16/9) = 3/5
f(a) = 2(cosa-2sina) = 2(3/5+4/5) = 16/5

Answer 2

朋友，弄错了吧，a是第四象限的角，那么tana＜0,不可能是4/3。

Answer 3

f(x) = {1-√2sin(2x-π/4)}/cosx
= {1-(√2sin2xcosπ/4-cos2xsinπ/4)}/cosx
= {1-(sin2x-cos2x)}/cosx
= {1-sin2x+cos2x}/cosx
= {1-2sinxcosx+2cos^2x-1}/cosx
= {-2sinxcosx+2cos^2x}/cosx
= 2(cosx-sinx)
=-2√2sin(x-π/4)

Answer 4

是14/5