(1) ∵向量a‖向量b,∴ sinθ*1-2*cosθ=0.
tan=2.
sec^2θ=1+tan^2θ=5 ,secθ=±√5.
cosθ=1/secθ=±√5/5.
∴cosθ=√5/5 θ∈(0,π/2).
∴ sinθ=√(1-cos^2θ)=2√5/5.
(2) sin(θ-ω)=sinθcosω-cosθsinω=3/5
2√5/5cosω-√5/5sinω=3/5.
2√5cosω -√5sinω=3.
√5 tanω=2√5-3secω
√ [5(sec^2ω-1)=2√5-3secω.两边平方,并化简得：
4sec^2ω-12√5secω+25=0.
secω={(12√5±√[(12√5)^2-4*4*25]}/2)4.
=(12√5±8√5)/8
sec ω1=5√5/2.
secω2 =√5/2.
cosω1=1/secω=2√5.
cosω2=2√5/5.