Question

已知向量a=(1+sin2x,sinx-cosx),b=(1,sinx+cosx),设函数f(x)=ab,若f(θ)=8

Answer 1

f(x)=1+sin2x+sin²x-cos²x=sin2x-cos2x+1=(根号2)sin(2x-π/4)+1

f(θ)=(根号2)sin(2θ-π/4)+1=8/5

所以sin(2θ-π/4)=3/10 (根号2)

cos2(π/4-2θ)=1-2sin²(π/4-2θ)=1-2* 9/50=16/25