Question

Confused??? on how to prove the equation, the first part of the problem

Answer 1

Asin(wt + φ) = c2sinwt +c1coswt

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 !