Answer:
Asin(wt + φ) = c2sinwt +c1coswt
Step-by-step explanation:
Proof:
wt here is periodic where as φ is constant
taking left hand side
Asin(wt + φ)
Using trigonometric identity sin(θ+φ) = sinθcosφ +sinφcosθ
Asin(wt +φ) = A[sinwtcosφ +sinφcoswt]
= Asinwtcosφ +Asinφcoswt
Now as we know φ is constant
so will Asinφ and Acosφ will also be constant
let Asinφ= c1
and Acosφ=c2
Putting in above expression, we get
Asin(wt +φ) = c2sinwt +c1coswt !
