How can we get this answer pls explain me the trignometric part For energy stored is electrical, we can write - Physics - Alternating Current

Question

How can we get this answer pls explain me the trignometric
part
For energy stored is electrical, we can write Q = Q
Hence, it can be inferred that the energy stored in the
capacitor is completely electrical at time, t =
(ii) Magnetic energy is the maximum when electrical energy,
Q′ is equal to 0
Hence, it can be inferred that the energy stored in the
capacitor is completely magnetic at time,

Jyoti Pant · Accepted Answer

Explanation of trigonometric part:

When total energy is equally shared between the inductor and capacitor,The energy stored in the capacitor is given by,=12×Maximum energy=12×Q'2C=12(Q22C)=14Q2CNow,Q'=Q2But given,Q'=Q cos2πTtSo, Q2=Q cos2πTtor  cos2πTt=12=cos(2n+1)π4 For n=0,1,2,
If n=0, cos(2n+1)π4=cosπ4=12If n=1, cos(2n+1)π4=cos3π4=12If n=2, cos(2n+1)π4=cos5π4=12so on
Thus, cos2πTt=cos(2n+1)π4or 2πTt=(2n+1)π4t=(2n+1)π4×T2π=(2n+1)T8