Signals & Systems | Plotting Magnitude and Phase Spectrum of Periodic Signal x(t) in Fourier Series

In this video Lecture, I have covered How to compute Fourier Series coefficients from the periodic signal?
Important Pointed to be noted for Conversion of sum of Sinusoids into single Cosine:
3 cos⁡(2t)+4 sin⁡(2t) can be converted into only r cos⁡(2t-Φ)
As sign between cos and sin terms is positive and we have to convert into cosine, so
r cos⁡〖(2t-Φ) = rcos(2t) cosϕ + rsin(2t)sinϕ〗
Thus, we can set, rcosϕ=3,rsinϕ=4 ,
By simplifying , r = √(3^2+4^2 ) = 5 ,& ϕ = tan^(-1)⁡〖(4/3)=〖53.1〗^o 〗
Hence, 3cos⁡(2t) + 4sin⁡〖(2t) = 5cos⁡(2t-〖53.1〗^o)〗
In video, I have followed another method and magnitude appeared as 2.5 which is incorrect. Please follow this method mentioned here for the conversion of sin and cos into single cosine. Thanks
Feel Free to ask any questions in the comment section. Contact me at fakhar.fast@gmail.com for any other help.
The link of this video can be found here [ https://youtu.be/9Tq04D6QdFo ]

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Видео Signals & Systems | Plotting Magnitude and Phase Spectrum of Periodic Signal x(t) in Fourier Series канала Fakhar STEM Sphere