The correct option is D √a+bab
Given ,
y=1√asinωt±1√bcosωt
We can re write the above equation as,
y=1√asinωt±1√bsin(π2+ωt)
This is a superposition of two waves, having phase difference ϕ=π2
∴ Resultant amplitude
R=√(A)2+(B)2+2ABcosϕ
⇒R=
⎷(1√a)2+(1√b)2+2π1√a×1√bcos90∘
⇒R=√1a+1b=√a+bab
Thus, option (d) is the correct answer.