Question

Prove the sin2O + cos²0 = 1​

Answer 1

Answer:

Step-by-step explanation:Let (C) be a unit circle, and M∈(C). Also, we will denote ∠IOM as θ (see the diagram). From the unit circle definition, the coordinates of the point M are (cosθ,sinθ). And so, OC¯¯¯¯¯¯¯¯ is cosθ and OS¯¯¯¯¯¯¯ is sinθ. Therefore, OM=OC¯¯¯¯¯¯¯¯2+OS¯¯¯¯¯¯¯2−−−−−−−−−√=cos2θ+sin2θ−−−−−−−−−−−√. Since M lies in the unit circle, OM is the radius of that circle, and by definition, this radius is equal to 1. It immediately follows that:

cos2θ+sin2θ=1