Prove the law of cosines c2 = a2+b2-2 a b cos C for a triangle

This video shows how to prove the law of cosines c2 = a2+ b2-2 a b cos C for a triangle. This formula can be used to calculate the sides and angles of a triangle

[harshagarwal]

after going trough tens of videos on this topic this is the video that made the concept crystal

[yogiHalim]

Third line typo there.
c²=b²-2.a.b.cosC + (a cosC)² + (aSinC)²
then
cosC²+sinC² = 1

[harshagarwal]

the only mistake is being written (aSinc)^2 twice

[ps_online]

from where did the other (asinC)² came