Please solve question number A-3. It is really urgent.

Recall that sin(x+y) = sin(x)cos(y)+sin(y)cos(x)

so

Rsin(wt+a) = Rcos(a)sin(wt) + Rsin(a)cos(wt)

we want to find

Rsin(wt+a) = e₁sin(wt) + e₂cos(wt)

so we can try to solve

Rcos(a) = e₁

Rsin(a) = e₂

To do that you first take the squares

R2cos2(a) + R2sin2(a) = e₁² + e₂²

By Pythagorean identity, cos2(a)+sin2(a) = 1

R2 =e₁² + e₂² , let's choose R = 

Hope it clears.............................